2006 2009 batch(cu5 ma)

(SHIFT I)
HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 620 002.
DEPARTMENT OF MATHEMATICS
CURRICULUM STRUCTURE (CAFETERIA)
B.SC., MATHEMATICS
( 2005 – 2008) (2006-2009)
1. Foundation Courses F
2. Major Compulsory and Optional courses M
3. Allied Compulsory and Optional courses A
4. Interdisciplinary Courses ID
5. Extra Projects and Placements.
Sem Com
ponent
Code No Course Subject Title Hrs/
Week
Credits
1 F1 CU5T:01 Language 1 –
Paper 1
5 5
F2 CU5E:01 Language II –
Paper 1
6 6
F3 RESCAPES Capacity Building 1 1
F4 Life Oriented
Education
1
M1 CU5MA:OM1 Major Core Calculus and Fourier Series 7 7
M2 CU5MA:OM2 Major Core Classical Algebra
&Trigonometry
6 6
A1 CU5MA:OA1A Allied Compulsory-
Paper 1
Mathematical Statistics-I 5 5
TOTAL 30 31
II F1 CU5T:E2 Language 1 –
Paper II
5 5
F2 CU5E:E2 Language II –
Paper II
6 6
F3 RESCAPES Environmental Studies 4
F4 Life Oriented
Education
1 1
M3 CU5MA:EM3 Major Core Analytical Geometry of
Three Dimensions and
Vector Calculus
7 7
M4 CU5MA:EM4 Major Core Sequences and Series 6 6
A2 CU5MA:EA2A Allied Compulsory
Paper II
Mathematical Statistics -II 5 5
TOTAL 30 34
1

III F1 CU5T:O3 Language I -
Paper III
5 5
F2 CU5E:O3 Language II –
Paper III
6 6
F3 RESCAPES Environmental Sustenance
Project
-- 1
F4 Life Oriented
Education
1 1
M5 CU5MA:OM5 Major Core Statics 4 4
M6 CU5MA:OM6A Major Core Differential Equations and
Laplace Transforms
5 5
A3 CU5MA:OA3A Allied Compulsory
Paper III
Mathematical
Statistics -III
5 5
ID1 Inter Disciplinary
Course
4 4
TOTAL 30 31
IV F1 CU5T:E4 Language I –
Paper IV
5 5
Paper IV
6 6
F3 RESCAPES Environmental Sustenance
Project
1
F4 Life Oriented
Education
1 1
M7 CU5MA:EM7 Major Core Dynamics 4 4
M8 CU5MA:EM8A Major Core Algebra 5 5
A4 Allied Optional
Paper I
5 5
Course
4 4
TOTAL 30 31
V F3 RESCAPES Impact Study 1
F4 Life Oriented
Education
1 1
M9 CU5MA:OM9 Major Core Real Analysis 5 5
M10 CU5MA:OM10A Major Optional Optimization
Techniques -1
5 5
M11 CU5MA:OM11A Major Optional Programming in C For
Numerical Methods
5 5
M12 CU5MA:OM12A Major Optional Numerical Methods 5 5
A5 Allied Optional
Paper II
5 5
Course
4 4
TOTAL 30 31
2

VI F3 RESCAPES Project
(optional)
F4 Life Oriented
Education
1 1
M13 CU5MA:EM13 Major Core Theory of Functions of a
Complex Variable
5 5
M14 CU5MA:EM14A Major Optional Optimization
Techniques - II
5 5
M15 CU5MA:EM15A Major Optional Introduction to Fuzzy
Mathematics
5 5
M16 CU5MA:EM16A Major Optional Graph Theory 5 5
A6 Allied Optional
Paper III
5 5
Course
4 4
TOTAL 30 30
SEMESTER – WISE CREDIT DISTRIBUTION
I SEMESTER 31
II SEMESTER 34
III SEMESTER 31
IV SEMESTER 31
V SEMESTER 31
VI SEMESTER 30
-------
188
3

B.Sc., MATHEMATICS
SEMESTER – I
MAJOR (CORE) – CALCULUS AND FOURIER SERIES
No. of Hours: 7 Max. Marks:100
No. of Credits: 7 CODE:CU5MA:OM1
UNIT I:
Successive differentiation – Leibnitz theorem (with proof) – Curvature – radius of curvature
– centre of curvature – circle of curvature (both in Cartesian and polar coordinates) and evolute.
UNIT II:
Partial differentiation – Total differential coefficient – Homogeneous functions-Partial
derivatives of a function of two functions – Jacobian of two and three variables-Maxima and
minima of functions of two variables.
UNIT III:
Reduction formulae: 0 ∫π/2
sinn
x dx, 0 ∫π/2
cosn
x dx, 0 ∫π/2
sinn
x cosn
x dx
Multiple integrals – Evaluation of double integrals in cartesian and polar co-ordinates. Triple
integrals (evaluation in Cartesian Co-ordinates only) - Change of order of Integration.
UNIT IV:
Beta and gamma functions – Definition, recurrence formula of gamma functions – Properties
of Beta functions-Relations between Beta and Gamma functions – Evaluation of simple integrals.
UNIT V:
Fourier cosine and sine series – Half range Cosine and Sine series.
TREATMENT as in
CALCULUS (Vol I) by S. Narayanan and T.K. Manicavachagom Pillay for units
I and II.
Unit I – Chapter III, Chapter X Sec2 (from 2.1 to 2.6)
Unit II- Chapter VIII (Sec 1 and Sec.4)
CALCULUS (Vol II) by S. Narayanan and T.K. Manicavachagam Pillay for units III and IV
Unit III- Chapter V Sections 1 to 4
Unit IV – Chapter VII Sections 2,3,4,5
Engineering Mathematics – Third year (Part B), 11th
Edition by Dr. M.K. Venkatraman for unit V.
Unit V – Chapter I (Section 1 to 6, Section 8, Section 10)
REFERENCES:
Schaums Outline series – Theory and problems of Advanced Calculus.
4

Differential and Integral Calculus by N. PISKUNOV Mir Publishers.
Advanced Calculus – David V. Widder – Prentice Hall of India
(II Edition)
Calculus and Analytic Geometry – Thomas/Finney Narosa Publishing House.
Calculus with Computer Applications:- Ransom V. Lynch,
Donald R. Ostberg & Robert G. Kuller.
Xerox College Publishing.
Schaums’ Outline series – Theory and Problems of Laplace Transforms.
********************************
5

B.Sc., MATHEMATICS
SEMESTER – I
MAJOR (CORE) – CLASSICAL ALGEBRA AND TRIGONOMETRY
CLASSICAL ALGEBRA
UNIT I:
Theory of Equations:
Relation between roots and coefficients – symmetric functions of roots in terms of the
coefficients –Sum of the powers of the roots of an equation-Newton’s Theorem on the sum of the
powers of the roots - Transformation of equations – Reciprocal equations – To increase or Decrease
the roots by a given quantity – Removal of terms – To form an equation whose roots are any power
of the roots of a given equation - Descarte’s rule of signs.
UNIT II:
Theory of Numbers:
Introduction – Divisors of a given number N – Euler’s function Ø (N) – highest power of a
prime p contained in n! – congruences – numbers in arithmetical progression – Fermats’ theorem-
Wilson’s theorem – Lagranges’ theorem.
TRIGONOMETRY
UNIT III:
Expansions of Cosnθ, Sinnθ, tannθ where n is a positive integer (excluding formation of
equations); Expansions of Cosn
θ, Sinn
θ in a series of sines and cosines of multiples of θ, (θ in
radians) and expansion of Cosθ, Sinθ, tanθ in a series of powers of θ – approximations.
UNIT IV:
Hyperbolic functions – in verse hyperbolic functions, separation into real and imaginary
parts. Logarithm of complex numbers x+iy – general value of logarithm.
UNIT V:
Summation of trigonometric series-method of differences – sum of sines of n angles in A.P.
– sum of cosines of n angles in A.P. – summation of series using complex quantities.
TREATMENT as in:
UNIT I: Algebra Vol I by T.K. Manicavachagom Pillay, T. Natarajan and K.S. Ganapathy
Chapter 6 Sec: 11 to 21,24.
UNIT II: Algebra Vol II by T.K. Manicavachagom Pillay, T. Natarajan and K.S. Ganapathy
Chapter 5 fully.
TREATMENT as in Trigonometry by Narayanan and Manicavachagom Pillay for UNIT III,
IV & V.
UNIT III: Chapter III (Formation of Equations Excluded)
UNIT IV: Chaper IV and in Chapter V (Sec 5 only)
UNIT V: Chapter VI (Sec. 1 to Sec.3)
REFERENCES:
1. Set Theory, Number System and Theory of Equations by Arumugam and
Thangapandi Issac, New Gamma Publishing House.
2. Trigonometry by P.R. Vittal, Margham Publisher.
3. Trigonometry by P.P. Gupta, Oxford University Press.
4. Trigonometry by P. Duraipandian, Emerald Publications.
6

****************************
B.Sc., MATHEMATICS
SEMESTER –II
MAJOR (CORE) – ANALYTICAL GEOMETRY OF THREE DIMENSIONS AND VECTOR
CALCULUS
No. of Credits: 7 CODE:CU5MA:EM3
UNIT I:
Cartesian coordinates- Distance between points – Direction Cosines – Direction ratios –
angle between two lines. The plane – the general equation of the plane – standard forms of
equations of planes – Equation of the plane in the form P+ λ P’ = Ø Bisector planes.
UNIT II:
Different forms of equations of a straight line – the plane and the straight line – coplanar
lines – the shortest distance between two skew lines – equations of two skew lines.
UNIT III:
Equation of a sphere – Length of the tangent from a point – Tangent planes. The plane
section of a sphere - Intersection of two spheres.
VECTOR CALCULUS
UNIT IV:
Differentiation:
Derivatives of vector functions – velocity and acceleration – differential operators –
directional derivatives, gradient, divergence and curl – solenoidal and irrotational vectors – vector
identities.
UNIT V:
Integration:
Integration of vector functions – velocity and acceleration – Line integrals – work done by a
force – conservative field – surface integral and its applications – volume integral and its
applications – Integral theorems (without proof ) - Gauss divergence theorem, Green’s theorem,
Stoke’s theorem and their applications.
Treatment as in “A Text Book of Analytical Geometry (Part II – Three Dimensions) By
T.K. Manicavachagom Pillay and T. Natarajan. Revised Edition 1996, Reprint July – 2000.
UNIT I: Chapters I and II
UNIT II: Chapter III (excluding sections 9,10 & 11)
UNIT III: Chapter IV for the Sphere
Reference:
Analytical Geometry (3 –Dimensional) by P.Duraipandian,Laxmi Duraipandian & D.Mahilan –
Emerald Publishers(1990)
For Vector calculus, Treatment as in “Vector Calculus” By K. Viswanathan and S. Selvaraj –
Emerald Publishers)
UNIT IV: Chapters 1 and 2
UNIT V: Chapters 3 and 4.
7

Reference:
Vector Analysis by P.Duraipandian ,Laxmi Duraipandian –Emerald Publishers (1998)
***********************************
B.Sc., MATHEMATICS
SEMESTER –II
MAJOR (CORE) – SEQUENCES AND SERIES
No. of Credits: 6 Code: CU5MA:EM4
UNIT I:
Sequences – sets – Sequences – Limit of a sequence – bounded sequences – Cauchy’s
general principle of convergence – monotonic sequence.
UNIT II:
Infinite Series- definition of convergence, divergence and oscillation – some general
theorems – convergence of 1/ np
and Geometric Series.
Tests of convergence. Comparison tests
1. Cauchy’s condensation test
2. D’Alembert’s Ratio Test
3. Cauchy’s Root test
4. Raabe’s test (simple problems only)
UNIT III:
Alternating Series : Absolute convergence – conditional convergence – Leibnitz’s test and
simple problems.
Binomial theorem for rational index – summation of series and approximations:
UNIT IV:
Exponential and Logarithmic Series – summation and approximations.
UNIT V:
General summation of series – Application of partial fractions –summation by difference
series – recurring series.
TREATMENT as in Algebra –volume I by Manicavachagom Pillay, Natrarajan & Ganapathy.
UNIT I: Chapter 2 – Section 4, Section 6, Section 7.
UNIT II: Chapter 2 – Section 8 to Section 20.
UNIT III: Chapter 2 – Section 21 to Section 24.
Chapter 3 – Section 5,10 & 14.
UNIT IV: Chapter 4
UNIT V: Chapter 5
REFERENCES:
1. A first course in Real Analysis by M.K. Singal and Asha Rani Singal,
R. Chand & Co, New Delhi.
2. Sequences and Series by Dr. Arumugam.
8

******************************
HOLY CROSS COLLEGE ( AUTONOMOUS) TIRUCHIRAPPALLI – 620 002.
B.SC., MATHEMATICS
SEMESTER III
MAJOR (CORE) : STATICS
No. of Hours: 4 Max.Marks:100.
No. of Credits:4 Code:CU5MA: OM5.
Unit : I
Force – Types of Forces – Equilibrium – Forces acting at a point Parallelogram of forces – Triangle
of forces Ploygon of forces - Lami’s theorem – Resolution of a force – Composition of forces –
Resultant – Conditions of equilibrium.
Unit: II
Parallel Forces – Like and Unlike parallel forces – Resultants – Moment of a force about a point -
Varignon’s Theorem on Moments – Principle of Moments – Moment of a force about an axis –
Couples – Equilibrium of two couples – Equivalence of two couples – Couples in Parallel Planes –
Resultant of Coplanar Couples – Resultant of a couple and a force.
Unit : III
Equilibrium of Three Forces acting on a rigid body – Three coplanar forces – conditions of
Equilibrium – Two trigonometrical theorems useful in the solution of statical problems – Problem
solving.
Unit : IV
Friction – Laws of friction – angle of friction – cone of friction – equilibrium of a body on a rough
inclined plane – Problems involving the force of friction.
Unit : V
Equilibrium of strings – Common catenary – equations – tension at any point – geometrical
properties – Parabolic catenary – Suspension Bridge.
Treatment as in Statics by Dr. M.K. Venkataraman, Agasthiar Publications, Trichy (1996).
Unit: I - Chapters 1 & 2
Unit: II – Chapters 3 & 4
Unit: III – Chapter 5
Unit: IV – Chapter 7
Unit: V – Chapter 11
BOOKS FOR REFERENCE
1.Statics by A.V. Dharmapadam
2.Mechanics by P. Durai Pandian & Others.
9

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPALLI - 2.
B.SC. MATHEMATICS
SEMESTER III
MAJOR (CORE ) : DIFFERENTIAL EQUATIONS AND LAPLACE TRANSFORMS
No.of.Hours: 5 Max.Marks: 100
No.of Credits:5 Code:CU5MA:OM6A
UNIT I :
ORDINARY DIFFERENTIAL EQUATIONS
Linear homogeneous equations with variable coefficients. Equations reducible to the linear
homogeneous equation. Method of variation of parameters.
UNIT II :
PARTIAL DIFFERENTIAL EQUATIONS
Formation of partial differential equations by eliminating arbitrary constant and functions -
solutions - General, particular and complete integrals - solutions to first order equations in four
standard forms – F(p, q) = 0, F(z,p,q) = 0, F(x,p,q) = 0,F(y,p,q) = 0, F1 (x,p) = F2 (y,q),
z = px+qy+f (p,q), Lagranges method of solving linear equation Pp + Qq = R.
UNIT III :
LAPLACE TRANSFORMS
Definition - Laplace transforms of functions eat
, Cosat, Sinat, tn
(n is a +ve integer), eat
cosbt,
eat
sinbt, f'(t), f''(t), fn
(t), tn
f(t), f(t)/ t
UNIT IV :
INVERSE TRANSFORMS
Inverse transforms relating to the above standard functions - application to solution of ordinary
differential equations with constant coefficients.
UNIT V :
Second order linear partial differential equation with constant coefficients - Particular integrals for
functions of the type e ax + by
, Sin (ax + by), Cos (ax + by), xr
ys
Application of partial differential equations - Solution to heat and wave equations by method of
separation of variables (No derivation of equations)
Treatment as in Differential Equations by Narayanan & Manicavachagom Pillay for Units I, II & III
UNIT:I Chapter V - Section 5 & 6 and Chapter VII - Section 4
UNIT:II Chapter XII ( Omit from Section 5.5)
UNIT:III Chapter IX – Sections 1 to 5
UNIT:IV Chapter IX – Sections 6 to 9
Treatment as in ENGINEERING MATHEMATICS Part B by Dr.M.K.Venkatraman for Unit V.
UNIT:V Chapter 2 ( Section 13 to Section 19 ) & Chapter 3 ( Omit from Section 10 )
*********************
10

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 2
B.SC. MATHEMATICS
SEMESTER : IV
MAJOR ( CORE ) : DYNAMICS
No. Of. Hrs: 4 Max. Marks:100
No. of Credits:4 CODE: CU5MA:EM7
UNIT: I
Momentum – Newton’s Laws of Motion – Absolute units of forces – Conservation of linear
momentum – Motion of a particle on planes – Motion of connected particles.
UNIT : II
Projectiles – Path of a projectile – Characteristics of the motion of a projectile – Greatest height -
Time of flight - Horizontal range – Maximum horizontal range – Directions of projection – Velocity
of the projectile – Simple problems.
UNIT : III
Motion of a projectile on an inclined plane – Range on an inclined plane – Time of flight – Greatest
distance from the inclined plane – Maximum range on an inclined plane – Directions of projection
on an inclined plane – Enveloping parabola – Simple problems.
UNIT : IV
Impulsive forces – Impact of two bodies – Motion of a shot and gun – Collision of elastic bodies –
Fundamental laws of inpact – Impact of a smooth sphere on a fixed plane – Direct impact – Oblique
impact – Simple problems.
UNIT : V
Simple harmonic motion in a straight line – Definitions – General solution of a simple harmonic
motion equation – Composition of two simple harmonic motions – Simple problems.
Treatment as in “A Text Book of Dynamics” by Dr. M.K. Venkatraman – Agasthiar Publications,
Tiruchy-2.
Eleventh Edition – February 2004.
Unit: I – Chapter IV – 4.1 to 4.18, 4.2 to 4.23
Unit:II- Chapter VI – 6.1 to 6.11
Unit:III – Chapter VI – 6.12 to 6.17
Unit:IV – Chapter VII – 7.1 to 7.5, Chapter VIII - 8.1 to 8.8
Unit:V – Chapter X – 10.1 to 10.3, 10.6, 10.7
BOOKS FOR REFERENCE:
1. Dynamics by Prof. M.L. Khanna - Jai Prakash Nathan & Company, Meerut – 10th
Edition –
1975.
2. Principles of Dynamics by Greenwood, Donald T-Prentice Hall of India-New Delhi – 1988.
3. Dynamics – K.Viswanatha Naik & M.S. Kasi – Emerald Publishers, Egmore, Chennai-2001.
4. Golden Dynamics by N.P. Bali – Laxmi Publishers, New Delhi – 1986.
11

B.SC. MATHEMATICS - SEMESTER IV / VI
MAJOR (CORE) : ALGEBRA
No. of. Hours : 5 Max.Marks : 100
No.of Credits: 5 Code: CU5MA:EM8A / CU5MA:EM15B
UNIT I:
Groups
Cosets and Lagrange's theorem - Normal subgroups and quotient groups - Finite groups and
Cayley tables - isomorphism and homomorphism.
UNIT II:
Rings:
Definition and examples - elementary properties of rings - ismorphism -types of rings -
Characteristic of a ring - subrings-ideals - quotient rings - homomorphism of rings
UNIT III:
Vector spaces
Definition and examples - subspaces - Linear transformation - span of a set - Linear independence
and Linear dependence.
UNIT IV:
Vector spaces ( Contn)
Basis and dimension – Maximal Linearly Independent set, Minimal Generating set, Isomorphism of
vector spaces - Rank and nullity - matrix of a linear transformation.
UNIT V:
Inner Product spaces
Definition and examples of inner product spaces, Orthonormal set, Gram – Schmidt
Orthogronalisation Process - Orthogonality - Orthogonal complement.
Treatment as in Modern Algebra by N. Arumugam and A. Thangapandi Isaac June 1997 - Edition
UNIT I: ( Chapter 3 - Sec.3.8 to 3.12)
UNIT II: ( Chapter 4 - Sec.4.1 to 4.8 & 4.10)
UNIT III: (Chapter 5 - Sec 5.1 to 5.5)
UNIT IV: ( Chapter 5 - Sec 5.6 to 5.8)
UNIT V: ( Chapter 6 - Sec 6.1 to 6.3)
1. A text book of Modern Abstract Algebra by Shanti Narayanan.
2. Modern Algebra by K. Sivasubramanian.
3. A text book of Modern Algebra by R. Balakrishnan & N. Ramabadran.
12

HOLY CROSS COLLEGE (AUTONOMOUS)TIRUCHIRAPALLI - 2.
B.SC. MATHEMATICS
SEMESTER V
MAJOR (CORE) REAL ANALYSIS
No.of.Hours : 5 Max.Marks: 100
No.of Credits:5 Code:CU5MA:OM9
UNIT I : REAL NUMBERS
Introduction to Real Number system - the field axioms and theorems - Order in R - Absolute value
- Completeness - Some important subsets of R - Representation of real numbers as points on a
straight line - Intervals - Countable and uncountable sets.
UNIT II : NEIGHBOURHOOD AND LIMIT POINTS
Neighbourhoods - Open sets - Closed sets - Limit points of a set - Closure of a set - Interior of a set
- Compactness and connectedness.
UNIT III : LIMITS AND CONTINUITY
Limits - Continuous functions - Types of discontinuities - Algebra and boundedness of continuous
functions - Intermediate value theorem - Inverse function theorem - Uniform continuity.
UNIT IV : DERIVATIVES
Introduction - Derivability and continuity - Algebra of derivatives - Inverse function theorem for
derivatives - Darboux's theorem.
MEAN VALUE THEOREMS
Rolle's theorem - Mean value theorems on derivatives (Lagrange's and Cauchy's) - Taylor's
theorem with remainder - Taylor's series - power series expansions of some standard functions: e ,
Sin x, Cos x, (1+x) and log(1+x)
UNIT V : RIEMANN INTEGRATION
13

Introduction - Riemann integrability and integral of bounded functions over bounded intervals -
Properties of Darboux sums - Darboux's theorems I and II - Equivalent definition of integrability
and integral - Conditions for integrability - Particular classes of bounded integrable functions -
Properties of integrable functions - Integrability of sum, difference, product, quotient and
modulus of integrable functions - Continuity and derivability of the integral function -
fundamental theorem of integral calculus.
Treatment as in 'A First Course in Real Analysis' by M.K.Singal and Asha Rani Singal - R.Chand &
Co. New Delhi. 20TH Edition,1998
UNIT I : CHAPTER 1
UNIT II : CHAPTER 2
UNIT III : CHAPTER 5
UNIT IV : CHAPTER 6 (Omit from section 6) and Chapter 8 ( Omit sections 7 and 8)
UNIT V : Treatement as in "Elements of Real Analysis" by Shanti Narayan.
Chapter 9 (Omit Sec 9.12, 9.13, 9.16 and 9.17)
1. 'A Course of Mathematical Analysis' by Shanthi Narayan.
3. "Real Analysis" by Arumugam and others.
14

B.SC. MATHEMATICS - SEMESTER V
MAJOR (OPTIONAL) OPTIMIZATION TECHNIQUES - I
No.of.Hours : 5 CODE:CU5MA:OM10A
No.of Credits: 5 Max Marks:100
UNIT I :
Mathematical formulation of the problem - Graphical solution methods - General Linear
Programming Problem - Slack and Surplus variables. Canonical and standard forms of L.P.P.
UNIT II :
The Simplex Method - Simplex Algorithm - Artificial variables - Charnes Method of penalties ( Big
- M method) - Problem of Degeneracy - Two-Phase Simplex method.
UNIT III :
Duality - Dual Simplex algorithm. Assignment Problem - Hungarian method - Unbalanced
assignment problem - Travelling Salesman Problem.
UNIT IV :
Transportation Problem - Initial basic feasible solution - Northwest corner rule - Row minima
method - Column minima method - Matrix minima Method - Vogel's approximation method -
Optimal solution - u - v method - Degeneracy - Unbalanced Transportation Problem.
UNIT V :
Introduction - Problem of sequencing - Problems with n jobs and Two machines - Problems with n
jobs and Three machines - problems with n jobs and m machines - Graphic solution.
Treatment as in "Operations research" by Kanti swarup,P.K.Gupta & Man mohan, Eighth
thoroughly revised edition.
UNIT - I - Chapter 2 (2.1 to 2.6)
UNIT - II - Chapter 3 - Section 3.1 to 3.5
UNIT - III - Chapter 3 - Section 3.6, Chapter 4 (Omit section 4.3) & Chapter 7.
UNIT - IV - Chapter 6
UNIT V - Chapter 10
15

B.SC. MATHEMATICS
SEMESTER V
MAJOR (OPTIONAL) PROGRAMMING IN C FOR NUMERICAL METHODS
No. of Credits:5 Code: CU5MA:OM11A
UNIT - I:
Constants, variables, data types, symbolic constants - operators and expressions - evaluation of
expressions - reading and writing a character - formatted input and output - handling of character
strings - operations on strings - string handling functions.
UNIT - II:
Decision making and branching - Using IF, IF-ELSE, Nesting of IF-ELSE statements - ELSE-IF
ladder - Switch statement - the conditional operator - GOTO statement - Decision making and
looping - the WHILE, DO, FOR statements.
UNIT - III:
Arrays - one dimensional, two dimensional, multi dimensional groups - structure - definition giving
values to members - Initialization - Comparison - arrays of structures - Arrays within structures -
structures within structures and functions - Unions - Size of structures.
UNIT - IV:
User defined functions - the form of C functions - Return values and their types - calling a function -
category of functions - no arguments and no return values - Arguments but no return values -
Arguments with return values - Nesting of functions - Recursion -
Function and arrays - the scope and life time of variables in functions.
UNIT - V:
File management - Defining and opening a file - Closing a file - I/O operations on files
Scope and Treatment as in "Programming in ANSI C " Second Edition By
E. Balagurusamy.
UNIT - I: Chapters 2,3,4 and 8
UNIT - II: Chapters 5 and 6
UNIT - III: Chapters 7 and 10
UNIT - IV: Chapter 9
UNIT - V: Chapter 12
16

REFERENCE BOOKS:
Programming in C - V.Rajaraman Programming with C - Schaum's Series
ANNEXURE
C Programming for Theory and Practicals:
Roots of equations : Iterative Methods
1. Bisection Method
2. False Position Mehod
3. Newton - Raphson Method
INTERPOLATION:
Lagrange's Method
Newton - Forward Method
Newton - Backward Method
NUMERICAL DIFFERENTIATION:
Euler Method
Predictor - Corrector Method
Runge-kutta IV order method
NUMERICAL INTEGRATION:
Simpson's 1/3 rule
Trapezoidal rule
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17

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI - 2.
B.SC. MATHEMATICS - SEMESTER V
MAJOR ( OPTIONAL ) NUMERICAL METHODS
No.of Hours : 5 Max.Marks : 100
No.of Credits:5 Code: CU5MA:OM12A
UNIT I
Solution of algebraic and transcendental equations:
Introduction - Bisection Method - Iteration Method - The Method of False Position - Newton -
Raphson Method - Generalized Newton's Method.
UNIT II:
Interpolation -Introduction -Finite Differences – Forward and Backward differences - Newton's
formula for interpolation - Central difference Interpolation formulae - Interpolation with
unevenly spaced points - Lagrange's interpolation formula.
UNIT III:
Numerical differentiation and integration:
Introduction - Numerical differentiation - Maximum and minimum values of a tabulated function -
Numerical integration – Trape zoidal rule - Simpson's 1/3-rule.
UNIT IV:
Solution of linear Systems of equations:
Introduction - Consistency of a linear system of equations - Solution of linear systems -Direct
methods - Matrix inversion method - Gaussian elimination method,Gauss - Jordan method - Gauss
- Seidel method.
UNIT V:
Numerical Solution of Ordinary Differential Equations:
Introduction - Solution by Taylor's series - Picard's method of successive approximations - Euler's
method - Modified Euler's method - Range-Kutta method - Predictor - Corrector method - Adams.
Moulton method - Milne's method.
Treatment as in 'Introductory Methods of Numerical Analysis' by
S.S.Sastry 21Printing, Second edition, April 1995.
UNIT I: Chapter 2 - Sec. 2.1 to 2.5.1
UNIT II: Chapter 3 - Sec. 3.1, 3.3, 3.3.1, 3.3.2, 3.6, 3.7, 3.7.1 to 3.7.4, 3.9, 3.9.1
UNIT III: Chapter 5 - Sec. 5.1 to 5.4.2 (Omit 5.2.1)
UNIT IV: Chapter 6 - Sec.6.1,6.2.5,6.3 to 6.3.2, 6.4.
UNIT V: Chapter 7 - Sec 7.1 to 7.6 (Omit 7.4.1)
REFERENCE :
Engineering Maths - Singharavelu. Numerical Analysis- Narayanan & Manicavachagom Pillai.
Numerical Methods - S. Arumugam, A. Thangapandi Isaac & A. Somasundaram
Numerical Methods in Science and Engineering – Dr. M.K. Venkataraman.
18

B.SC. MATHEMATICS
SEMESTER VI
MAJOR ( CORE ) THEORY OF FUNCTIONS OF A COMPLEX VARIABLE
No.of Hours : 5 Max Marks:100
No.of Credits:5 Code: CU5MA:EM13
UNIT I :
Analytic functions
Introduction - Definition - Continuous functions - Convergence of sequences and series absolute
convergence - Uniform convergence - Cauchy - Riemann equations.
UNIT II :
Bilinear Transformations:
Elementary transformation - Bilinear transformation - Cross ratio - Fixed points of Bilinear
transformation - some special bilinear transformation.
UNIT III :
Integration in the complex plane :
Complex integration - Cauchy's integral theorem (Reimann’s proof only) and its extension -
Cauchy's integral formula - Derivative of analytic functions - Morera's theorem - Cauchy's
inequality for fn
(z0), Liouville's Theorem.
UNIT IV :
Expansion of functions in Power Series
Taylor's theorem - Laurent's theorem - Singular points - Zeros - Pole - Essential singularity
- Meromorphic function - Principle of the argument - Rouche's theorem - Fundamental Theorem of
Algebra.
19

UNIT V :
Residue Theorem and Contour Integration
Residue at a pole - Residue theorem - Evaluation of Definite Integrals between limits
(-∝ to ∝ ) - Extension of the Result- Jordan's lemma ( Statement only)- Evaluation of
∫ Sinax f(x) dx, ∫ Cosax f(x)dx where a > 0 and (i) f(z) does not have a pole on the real axis
(ii) f(z) have poles on the real axis (Only Semi Circular contour is included).
UNIT I, III to V:
Treatment as in "Complex Analysis" by S.Narayanan & T.K. Manicava chagam Pillay, Revised 3rd
Edition,1985 .
UNIT I: Chapter 1(Omit section 8)
UNIT III : Chapter 3 ( Omit section 13 & 14 )
UNIT IV : Chapter 4
UNIT V : Chapter 5 - sec 1 to 7
UNIT II:
Treatment as in " Complex Analysis" by S.Arumugam, A.Thankapandi Isaac and A.Somasundaram.
CHAPTER 3 (Sec.3.1 To 3.5)
1. Functions of a Complex Variable - E.G. Phillips.
2. Complex Analysis - P.Duraipandian and Laxmi Duraipandian.
3. Complex Variable - Churchill.
4. Theory of functions of a Complex Variable - Shanthi Narayanan.
5. Complex Analysis by Sridharan.
*******************
20

B.SC. MATHEMATICS
SEMESTER VI
MAJOR (OPTIONAL) OPTIMIZATION TECHNIQUES -II
No.of Credits:5 Code: CU5MA:EM14A
UNIT - I:
Game theory - Two person zero - sum games - the maximin and minimax principle -
saddle points - graphical solution of 2 X n and m X 2 games Dominance property.
UNIT - II:
Queueing theory - Poisson process and exponential distribution - classification of queues -
Poisson queues.
UNIT - III:
Inventory control - types of inventory - Economic order quantity - Deterministic inventory
problem - EOQ problem with price breaks.
UNIT - IV:
Multi-item deterministic problem - Inventory problem with uncertain demand - systems of
inventory control (Q system and P system) Probabilistic inventory problems.
UNIT - V:
Network scheduling by PERT - CPM time calculations in Networks -Critical path method
( CPM ) - PERT calculation. Scope and treatment as in "Operations Research" By
antiswarup, P.K.Gupta and Manmohan, Eighth thoroughly revised edition.
UNIT - I: Chapter 9 ( Sec 9.1 to 9.7)
UNIT - II: Chapter 17 ( Sec 17.1 to 17.8)
UNIT - III: Chapter 18 ( Sec 18.1 to 18.7)
UNIT - IV: Chapter 18 ( Sec 18.8 to 18.11 )
UNIT - V : Chapter 21 ( Sec 21.1 to 21.7 )
*************
21

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 2
B.SC., MATHEMATICS
VI – SEMESTER.
MAJOR (OPTIONAL) INTRODUCTION TO FUZZY MATHEMATICS
.
NO. OF HOURS:5 MAX. MARKS:100
NO. OF CREDITS:5 CODE: CU5MA:EM15A
UNIT I :
Fuzzy Set Theory- Introduction-Concept of a fuzzy set-Relation between fuzzy sets-
Numbers and Crisp set associated with a fuzzy set-Fuzzy sets associated with a given fuzzy
set- Extension Principle.
UNIT II:
Operations on Fuzzy Sets-Introduction-Fuzzy Complement- Fuzzy Union-Fuzzy Intersection
UNIT III :
Fuzzy Relations-Introduction- Operations on Fuzzy Relations-α-cuts of Fuzzy Relations-
Compositions of Fuzzy Relations-Projections of Relations-Cylindric Extensions.
UNIT IV :
Fuzzy Logic- Introduction-Three valued logics-N valued logics for N>4- Infinite valued
logics- Fuzzy logic-Fuzzy Propositions and Rules- Reasoning.
UNIT V :
APPLICATIONS:
Fuzzy methods in Control Theory-Introduction-Fuzzy Expert Systems-Classical Control
Theory Vs Fuzzy Control Theory-Examples-Components of FLC-Formulation of FLC.
BOOKS FOR STUDY:
For Units I,III,IV & V:
“Introduction to Fuzzy Sets and Fuzzy Logic” By M.Ganesh –Edition2006-Prentice Hall of
India Pvt. Limited, New Delhi.
UNIT I : CHAPTER 6 - Secs. 6.1 to 6.9.
UNIT III : CHAPTER 7 - Secs. 7.1 to 7.7
UNIT IV : CHAPTER 8 - Secs. 8.1 to 8.8
UNIT V : CHAPTER 9 - Secs. 9.1 to 9.8
For Unit II
Treatment as in Fuzzy Sets and Fuzzy Logic –Theory and Applications by
George J .Kler /Bo yuan.
UNIT II : Chapter 3 secs (3.1 to 3.4)
BOOKS FOR REFERENCE :
1. Introduction to the theory of A.Kaufmann ,Academic press ,Newyork .
2. “Fuzzy Set ,Uncertainity and information “by Klir &Bouyal .
22

3. “Uncertainity and Fuzzy Logic” by George J.Klir & Bo yuan.
4. T.M.Ross ,Fuzzy Engg.Application TMH.
B.SC. MATHEMATICS - SEMESTER VI
MAJOR ( OPTIONAL) GRAPH THEORY
No.of Hours : 5 Max Marks:100
No.of Credits:5 Code:CU5MA:EM16A
UNIT I :
Introduction- graphs and subgraphs-isomorphism- Ramsey numbers – Independent sets and
coverings - intersection graphs and line graphs - Matrices - Operations on graphs.
UNIT II :
Degree sequence-graphic sequences-walks, trails and paths-connectedness & components-blocks-
connectivity.
UNIT III :
Eulerian and Hamiltonian graphs and trees.
UNIT IV :
Directed Graphs :
Introduction – Definitions and Basic Concepts –Paths and Connections –Digraphs and Matrices –
Tournaments .
UNIT V :
Applications of Graph Theory :
Introduction –Connector Problem –Shortest Path Problem –Transformation and kinematic Graph –
Designing One Way Traffic System – Applications - The travelling salesman problem – Job
sequencing problem.
Treatment as in "Invitation to Graph Theory" by Dr.S.Arumugam and Dr.S.Ramachandran 1994
edition.
UNIT I : Chapters 1 and 2
UNIT II : Chapters 3 and 4
UNIT III : Chapter 5 and 6
UNIT IV : Chapter 10
UNIT V : Chapter 11
1. Graph theory by Harary, Narosa Publishing House New Delhi, Bombay.
2. Graph theory with applications to Engineeering and Computer Science by
Narsingh Deo, Prentice Hall of India, New Delhi.
23

ALLIED: MATHEMATICAL STATISTICS - I
No. of Credits: 5 CODE:CU5MA:OA1A
UNIT I:
Definition of Statistics – Statistical data – primary and secondary – collection, classification and
tabulation of data. Diagrammatic and graphical representation.
UNIT II:
Measures of dispersion – calculation of Mean Deviation, Quartile deviation, standard deviation,
coefficient of variation and moments for frequency distributions- concept of skewness and kurtosis
and their measures.
UNIT III:
Simple Correlation – rank correlation – Linear regression. (Error analysis in chapter 12 omitted)
UNIT IV:
Curve Fitting – Fitting straight lines and parabolic curves by the method of least squares and Index
Numbers- Uses – Types – Laspeyre’s, Paache’s, Fisher’s and Marshall
Edgeworth methods-Tests of Consistency – Chain Base Index – Fixed Base Index-Cost of Living
Index – Aggregate Expenditure Method – Family Budget Method .
UNIT V: Analysis of time series- Secular Trend-Seasonal Variation-Cyclical Variation – Irregular
Variation.
TREATMENT as in “Statistics” by R.S.N. Pillai and V. Bagavathi,
S.Chand & Co, New Delhi
UNIT I: Chapter 1,2,4,6, to 8
UNIT II: Chapters 10 and 11
UNIT III: Chapter 12 and 13 (Omit “Error analysis” in Chapter 12)
UNIT IV: Chapter 11 Section 11,9,4 & Chapter 14
UNIT V: Chapter 15.
REFERENCES :
1. Business Mathematics and Statistics by P.A. Navaneetham, Jai Publishers.
2. Statistics by M.C. Shukla and S.S. Gulshan, S.Chand & Co, New Delhi.
3. Advanced Practical Statistics by S.P. Gupta, S.Chand & Co, New Delhi.
**************
24

ALLIED : MATHEMATICAL STATISTICS - II
No. of Credits: 5 CODE: CU5MA:EA2A
UNIT I: Random Variables
Discrete and continuous random variable, cumulative distributive function, properties of distribution
function, function of a random variable, two dimensional random variable, joint probability
function, marginal probability distribution, conditional probability distribution, independent random
variables.
UNIT II: Expectation and Variance
Expectation of a random vaiable - expectation of a function of a random variable, theorems on
expectation. Variance – definition, theorems on variance, Tchebychev’s inequality.
UNIT III:
Moments and Moment Generating Function, Characteristic Function
Moments – definition, relation between central and raw moments, Moment generating function,
properties of moment generating function. Characteristic function – definition properties of
characteristic function, moments from characteristic function, characteristic function of some
special type of random variables, characteristic function of sum of independent random variables,
inversion theorem on characteristic function.
(Probability generating function and cumulants are excluded)
UNIT IV: Discrete Distributions
Binomial distribution – Definition, properties, binomial frequency distribution, moments, recurrence
formula for moments, moment generating function, additive property, mode.
Poisson distribution – Definition, properties, Poisson frequency distribution, Poisson distribution as
limiting form of binomial distribution, moments, recurrence formula for moments, moment
generating function, mode.
Unit V – Continuous distributions
Normal Distribution – Definition, moments, moment generating function, linearity property, mean
deviation, mode, points of inflection, normal probability integral, properties of normal distribution.
Uniform distribution – Definition, mean, variance, moment generating function.
Exponential distribution – Definition , mean, variance, median, moment generating function.
TREATMENT as in Mathematical Statistics by Dr. P.R. Vittal, Margham Publications, T.Nagar,
Chennai – 600 017. (2002 Publication)
Unit I - Chapter 2
Unit II - Chapters 3, 4
Unit III - Chapters 5, 6 (Probability generating function and cumulants are excluded)
Unit IV - Chapters 12, 13
Unit V - Chapters 16, 17, 18
REFERENCES:
1. Mathematical Statistics by Gupta & Kapoor
2. Mathematical Statistics by S. Venkataraman & P.R. Vittal.
25

ALLIED : MATHEMATICAL STATISTICS - III
No. of Credits: 5 CODE: CU5MA:OA3A
UNIT I:
Sampling distribution –Chisquare, student-t and F distributions.
UNIT II:
Point Estimation – unbiased estimator, efficient estimator, Cramer- Rao inequality, Rao – Blackwell
theorem, consistent estimator, sufficient estimator, method of moments, method of maximum
likelihood.
Interval Estimation – Confidence interval for the mean of the normal population, for the difference
between means, for the proportion of population, for the difference between two proportions.
UNIT III:
Large samples – definitions, test of hypothesis – test for a specified mean, for the equality of a
means, for specified proportion, for the equality of 2 proportions, for standard deviation of the
population, for equality of two standard deviations, for correlation coefficient.
UNIT IV:
SMALL SAMPLES : t Test for a specified population mean, for difference between two population
means, for paired observations.
F test – for Equality of two population variances, (Analysis of variance excluded).
UNIT V:
SMALL SAMPLES: Chi square Test – definition, additive property, Pearson’s Statistics, Uses of
Chi-square test, test for a specified population variance, test of independence of attributes. Test of
goodness of fit.
TREATMENT as in Mathematical Statistics by dr. P.R. Vittal, Margham Publications, T.Nagar,
Chennai – 17.
UNIT : I - Chapter 22
UNIT : II - Chapter 23
UNIT : III - Chapter 24
UNIT : IV - Chapter 25,26
UNIT : V - Chapter 27.
26

ALLIED MATHEMATICS PAPER I
No. of Credits: 5 CODE:CU5MA:OA1B
UNIT I : ALGEBRA
Matrices – Rank of a Matrix of order 2 and 3 Consistency of a system of linear non-homogeneous
equations- Characteristic equation of a square matrix – Evaluation of eigen values and eigen vectors
– Cayley – Hamilton theorem (without proof) and simple problems.
UNIT II : TRIGONOMETRY
Expansions of Cosnθ, Sinnθ and Tannθ (n being a positive integer) – Expansions of Sinnθ and
Cosnθ in a series of sines and cosines of multiples of θ (n being a positive integer and θ in radians) –
Expansions of Sinθ, Cosθ and Tanθ in a series of powers of θ – approximations (Formation of
equations excluded)
UNIT III :
Hyperbolic functions, inverse hyperbolic functions, separation into real and imaginary parts,
Logarithms of complex numbers of the form x+iy and general value of logarithms.
UNIT IV : DIFFERENTIAL CALCULUS
Successive differentiation – nth derivative of standard functions – Leibnitz theorem (without proof)
Application to simple problems – Jacobians of two and three variables.
UNIT V : MULTIPLE INTEGRALS
sinn
x dx, 0 ∫π/2
cosn
x dx, 0 ∫π/2
sinn
x cosn
x dx (Problems only)
Introduction to evaluation of double (Change of order of integration excluded) and Triple integrals
(in Cartesian only).
TREATMENT as in Ancillary Mathematics by S. Narayanan and T.K. Manicavachagom Pillay.
REFERENCES:
1. A Text –Book on Algebra-I by Rs.S.Aggarwal Published by S.Chand &
Company(Pvt)Ltd.,New Delhi (1989).
2. A Text-Book on Trigonometry by P. Balasubrahmanyam, P.R. Venkatachary & G.R.
Venkataraman, Published by ROC House & Sons(1972).
3. A Text – Book on Differential Calculus by H.S. Dhami, Published by New Age
International(P) Limited, New Delhi(1998).
27

ALLIED MATHEMATICS PAPER II
No. of Credits: 5 CODE: CU5MA:EA2B
Analytical Geometry of Dimensions:
UNIT I:
Cartesian co-ordinates – distance between points – Direction Cosines – Direction ratios –
angle between two lines - The Plane – the general equation of the plane – Standard forms of
equations of planes.
UNIT II:
Skewlines – Shortest distance between two skewlines – equation of the line of shortest
distance (Cartesian only) – coplanarity of Straight lines Sphere. General equation – tangent planes
– section of a sphere by a plane - sphere through a given circle.
Vector Calculus:
UNIT III: VECTOR DIFFERENTIATION
Velocity – acceleration – scalar and vector fields – Gradient, Divergence and curl –
applications - Laplacian operator.
UNIT IV: VECTOR INTEGRATION
Line integral – surface integral – volume integral – application of Gauss and Stoke’s
theorems (Statement only) simple problems.
UNIT V: FOURIER SERIES
Fourier series – full range and half range series Solution of wave equation and one
dimensional heat equation by the method of separation of variables.
TREATMENT as in
UNIT I & II : Ancillary Mathematics by S. Narayanan and others.
UNIT III & IV : Vector analysis by K. Viswanathan and S. Selvaraj.
UNIT V: Engineering Mathematics (Third year – Part B) by Dr. M.K. Venkatraman.
********************
28

ALLIED MATHEMATICS PAPER III
No. of Credits: 5 CODE: CU5MA:OA3B
UNIT I : Partial Differential Equations
Formation of equations by eliminating arbitrary constants and arbitrary functions; definition
of general, Particular, complete and singular integrals – solutions of first order equations in their
standard forms – F(p,q) = 0, F(x,p,q) = 0, F(y,p,q) = 0, F(z,p,q) = 0,
F(x,p) = F (y,q), Z = px+qy+f(p,q), Lagrange’s equations Pp+Qq = R
UNIT II : Laplace Transform
Laplace transforms of the functions eat
, e-at
, cosat, sinat, tn
, e-at
cosbt, e-at
sinbt, e-at
tn
,
f’(t), f”(t), fn
(t) (where n is a positive integer)
Inverse Transforms
Inverse transforms relating to the above standard functions – application to solution of
ordinary differential equations with constant coefficients.
Unit III: Numerical Methods
(Derivation of formulae not expected)
Interpolation – shift operator – Newton’s forward difference formula – backward difference
formula Lagrange’s formula.
Unit IV: Statistics
Measures of dispersion – Range – Quartile deviation – Mean deviation – Standard deviation
and their coefficients.
Correlation Coefficient
Karl Pearson’s coefficient – Definition and evaluation (frequency distribution not included)
and Spearman’s rank correlation.
Unit V
Simple linear regression – definition, stating properties on regression lines and problems.
29

Tests of significance based on normal distribution – difference between proportions –
difference between means – difference between standard deviations (Problems only)
TREATMENT as in
Ancillary Mathematics (Volume I – Part II Section B) by Narayanan and T.K. Manicavachagom
Pillay (Printed in 1990) for units I and II.
Unit I : chapter 5 under differential equations section
Unit II: chapter 4 under differential equations section
Introductory Methods of Numerical Analysis (second Edition) by S.S. Sastry for units III.
Chapter 3 sections 3.1, 3.3, 3.5, 3.9, 3.9.1
Statistics by R.S.N. Pillai and Bagavathy for Unit IV& V.
*******************
30

APPLIED MATHEMATICS – I
NO. OF HOURS/WEEK: 5 MAX. MARKS : 100
NO. OF CREDITS: 5 CODE: CU5MA:OA1C
UNIT : I
Matrices and Determinants: Product of determinants – Solution of system of linear equations-
Cramer’s rule-matrixes – linear independents and dependence – Eigen values and Eigen vectors of a
matrix – Cayley Hamilton’s Theorem(without proof).
UNIT : II
Differential Equation: First Order: Variable separable – Homogeneous and non – homogeneous
equations – linear type equations – Bemoulli’s equations.
UNIT : III
Second Order: Particular integrals – methods for finding particular integrals – all types of equations
including variable coefficients (Second Order only).
UNIT : IV
Laplace Transforms: Definition – properties – sufficient conditions – Laplace Transform of periodic
functions – solving differential equations using Laplace Transforms – the inverse transforms.
UNIT : V
Fourier Series: Fourier Series: – Even and odd functions – properties of odd and even functions –
Half range Fourier series – Development in sine and cosine series (omitting general interval).
BOOK FOR STUDY:
Unit : I
1. “Ancillary Mathematics – Volume 1 - Part I – Algebra”,
S. Narayanan, R. Hanumantharao, T.K. Manicavachagom Pillay &
Kandaswamy.
Unit II, III & IV:
2. Narayanan and Manickavasagam Pillai, “Ancillary Mathematics Volume 1 :
Part II (Section B)-Integral Calculus and Differential equations.
Unit V:
3. Dr. M.K. Venkataraman, “Engineering Mathematics (Vol II)”, Third Edition,
1988.
31

APPLIED MATHEMATICS – II
NO. HOURS/WEEK: 5 MAX. MARKS : 100
NO. OF CREDITS:5 CODE: CU5MA:EA2C
Unit I:
Definition-Axiomatic approach to probability-Finite sample space-Conditional probability-
Multiplicative law of probability-probability of an event in terms of conditional probability-Baye’s
theorem-Independence events.
Chapter 18 in book 1(page no:582-613)
Chapter 1 in book 2:(page no:1-33)
Unit II:
Binomial distribution-Poisson distribution-Properties of distributions(only mean,variance and
standard deviation)-Practial problems under distributions.
Unit III:
Continuous distributions-Normal distribution-Beta distribution-Gamma distribution(practical
problems only).
Unit IV:
Test of significance based on normal distribution-Difference between proportions-Difference
between means-Difference between standard deviation(problems only).
Unit V:
Analysis of time series:
Definition-Uses-Time series models-Secular trend-Seasonal variation-Preparation of data for
analysis-Measurement of secular trend-Graphic method of least squares-Parabolic curve-Shifting the
origin-Logarithmic trend-Measurement of seasonal variations-Method of simple average-Practical
problems.
Chapter 15 in book 1(page no:470-501)
Books for study:
1.Statistics(theory and practice)third edition 1993 by Mr.R.S.N.Pillai & V.Bagavathi
2.Mathematical Statistics first edition 1973(reprint 1974)by S.Venkataraman & P.R.Vital.
3.Statistics by Mr.R.S.N.Pillai & V.Bagavathi
32

APPLIED MATHEMATICS – III
NO. HOURS/WEEK: 5 MAX. MARKS : 100
NO. OF CREDITS:3 CODE: CU5MA:OA3C
UNIT : I
INTERPOLATION:
Newton Gregory forward and backward interpolation formulae-Lagrange’s Interpolation formula.
Solving algebraic and transcendental equations – Bisection, False position and Newton Raphson
methods.
UNIT : II
SOLVING SIMULTANEOUS EQUATIONS:
Gauss elimination – Finding inverse of a matrix using Gauss elimination method – Iterative
methods. Gauss Jacobi and Gauss Seidal methods.
UNIT : III
Trapezoidal rule and simpsons 1/3 rule. Solving differential equations (1st
order differential
equations only) – solutions by Euler’s method – runge Kutta 2nd
and 4th
order method.
UNIT : IV
MEASURES OF LOCATION:
Mean – Median – Mode – Measures of variation: Range – standard deviation – Coefficient of
Skewness.
UNIT : V
ASSOCIATION OF ATTRIBUTES:
Yules coefficient of association. Correlation coefficient – rank correlation.
Note: Stress May be on the application problems.
BOOK FOR STUDY:
Unit I, II & III:
1. Dr. M.K. Venkataraman, “Numerical Methods in Science and Engineering”, 2nd
Edition,
1987.
Unit IV & V:
2. R.S.N. Pillai and V. Bagavathi, “Statistics”, S. Chand and Co. Ltd., 1995.
33

ALLIED: BUSINESS MATHEMATICS
No. of Credits: 5 CODE:CU5MA:OA1D
UNIT I:
Mathematics of finance – Simple interest – Recurring deposit – Compound interest –
Depreciation – discounting.
UNIT II:
Matrices - inverse of a matrix rank of a matrix – solution of a system of three linear
equations- Arithmetic and geometric progressions – finding nth term and sum to n terms only.
UNIT III:
Differentiation – Applications of the derivative - Integration with applications.
UNIT IV:
Transportation problem – Initial basic feasible solution – North West Corner rule – Vogel’s
Approximation method – Matrix minima method (optimal solution excluded)
UNIT V:
Assignment problem (Travelling salesman problem excluded) – Sequencing problems
(Problems with n jobs and 2 machines only)
TREATMENT as in
Business Mathematics and Statistics by Prof. P.A. Navaneetham, Jai Publishers.
(Chapters 1,2,4 (excluding section 13), 6,7 (Sections 1 and 2 and 4 only) and
8 (upto section 7 only) for Units I, II and III
UNITS IV & V
Operations Research by Kanti Swarup, P.K. Gupta, Man Mohan,
Sultan Chand & Sons, New Delhi.
Chapter 6, Section 6.1 & 6.5
Chapter 10 Sections 10.1, 10.2 and 10.3
REFERENCES:
1. Algebra by T.K. Manicavachagom Pillay, T. Natarajan, K.S. Ganapathy,
S. Viswanathan – Printers & Publishers Private Limited, Chennai.
2. Business Mathematics by B.M. Aggarwal, Sultan Chand & Sons, New Delhi.
3. Problems in Opperations Research by P.K. Gupta, D.S. Hira,
S.Chand & Co, New Delhi.
34

4. Linear Programming by M.K. Venkataraman, The National Publishing Company, Chennai.
**************
ALLIED: BUSINESS STATISTICS
No.of Hours:5 Max. Marks:100.
No. of Credits:5 Code:CU5MA:EA2D
UNIT:I
Introduction - Collection of Data - Classification and Tabulation - Diagrammatic representation.
UNIT:II
Measures of Dispersion - Range - Quartile Deviation - Mean Deviation - Standard Deviation -
Relative measures - Measures of Skewness and Kurtosis.
UNIT:III
Correlation - Scatter Diagram - Karl Pearson's Coefficient of Correlation - Rank Correlation -
(Correlation of a bivariate fequency distribution and Coefficient of concurrent Deviation to be
excluded)
Regression - Properties, Regression lines and problems.
UNIT:IV
Time Series - components of Time Series - measurement of trend - measures of seasonal
variation – problems (Deseasonalization is excluded)
UNIT:V
Index Numbers - methods of construction of Index Numbers - tests for Index Numbers - cost of
living Index Number - uses of Index Numbers – general problems in the construction of Index
Numbers. (Shifting of Base and Splicing of Index Numbers are excluded)
Treatment as in Business Statistics by Dr. P.R. Vittal
UNIT I - Chapters 1 to 4
UNIT II - Chapters 6, 7
UNIT III - Chapters 8, 9
UNIT IV - Chapter 13
UNIT V - Chapter 14
35

HOLY CROSS COLLEGE (AUTONOMOUS) TRICHIRAPPALLI – 620002
SEMESTER-I
ALLIED- BUSINESS MATHEMATICS & STATISTICS
No of hours :5 Max marks : 100
No of Credits :5 Code : CU5MA:OA1E
UNIT I :
Application of derivatives –marginal functions –elasticity –increasing and decreasing
functions –maxima and minima –Linear Programming Problem–formulation & graphic solution .
UNIT II :
Transportation Problem –North-West Corner Rule –Matrix minima method-Vogels
approximation method (only initial basic feasible solution ) –Assignment Problem –Hungarian
method.
UNIT III :
Statistics –meaning and scope –collection of data –classification and tabulation –diagrams
and graphs –histogram-polygon –cumulative frequency curves .
UNIT IV :
Measures of dispersion –range, quartile deviation ,mean deviation standard deviation –merits
demerits –Karl Pearsons coefficient of correlation ,Rank correlation –Regression(Raw data only).
UNIT V :
Index numbers
Treatment as in “ Statistics “ By R.S.N Pillai and V.Bagavathi for
Units I , II & III
And “ Business Mathematics “ by P.A. Navaneetham &“ Operations Research “ by Kanti Swarup ,
Man Mohan & P.K Gupta for Units IV & V
REFERENCES:
1. A Text-Book on Business Statistics by G.V.Shenoy, U.K. Srivastava & S.C.Sharma
Published by V.S. Johsi for wiley Eastern Limited, New Delhi(1998).
2. A Text – Book on Business Statistics by M.Wilson, Published by Himalaya,
Mumbai(2003).
36

ALLIED : BUSINESS MATHEMATICS & STATISTICS FOR MANAGERS
No.of Hours:5 Max. Marks:100
No.of Credits:5 Code:CU5MA:EA2F
Unit I :
Mathematics of finance-Simple Interest-Recurring Depoist-Compound Interest-
Depreciation-Discounting.
Unit II :
Differentiation-Applications of the derivative-Integration with applications. .
Unit III :
Statistics-Meaning & scope- Collection of data- Classification & Tabulation-
Diagram&Graphs(Histogram,polygon, Cumulative) Measures of central tendency,
(Mean,Median,Mode).
Unit IV:
Measures of Dispersion(Range,Quartile Deviation, Mean deviation, Standard deviation
,Correlation- Co-efficient- Regression equation.
Unit V:
Index Numbers - methods of construction of Index Numbers - tests for Index Numbers -
cost of living Index Number - uses of Index Numbers – general problems in the construction of
Index Numbers. (Shifting of Base and Splicing of Index Numbers are excluded)
BOOKS FOR STUDY:
TREATMENT as in
UNIT I & II,III : Business Mathematics and Statistics by P.R.Navaneethan.
UNIT IV,V: - Business Statistics by P.R.Vittal.
37

SEMESTER – IV
ALLIED (OPTIONAL) :FORTRAN 90 AND ITS APPLICATIONS
No. Of. Hrs:5 Max. Marks:100
No. of Credits:5 Code:CU5MA :EA4A
UNIT: I :
FORTRAN Numeric constants – scalar variables – declaration – named constants .
Arithmetic operators - integer expressions - real expressions - precedence of operators in
expressions - assignment statements - intrinsic functions .
UNIT : II
Conditional Statements - relational operators – The BLOCK IF construct .
Elementary Format Specifications - Format description for numerical DATA ( READ
Statement )- Format description for PRINT Statement - Multi record formats – Printing character
strings -Reading and writing logical quantities.
UNIT : III
Implementing Loops in Programs - The BLOCK DO Loop - Count controlled DO Loop -
Rules regarding Do Loops.
UNIT : IV :
Logical expressions and more control statements - Logical constants, variables and
expressions-precedence rules for logical operators - The CASE statement.
Defining and manipulating Arrays –Arrays variables –use of multiple subscripts –DO type
notations for INPUT / OUTPUT statements –initialising Arrays –terminology used for
multidimentional Arrays.
UNIT : V :
Functions and Subroutines - Function Subprograms- Syntax rules for Function
Subprograms - Generic functions.
Subroutines - Internal procedures –Comparison of Function Subprograms and
Subroutines.
38

TREATMENT AS IN Computer Programming in FORTRAN 90 and 95 by V. Rajaraman
UNIT I : CHAPTERS 3 AND 4 (Omit 4.8 )
UNIT II : CHAPTERS 6 AND 11 ( Omit 11.6 and 11.7 )
UNIT IV : CHAPTERS 8 AND 10 (Omit 10.7 and 10.8 )
UNIT V : CHAPTER 9
ANNEXURE : PROGRAMS (only the following programs are expected )
UNIT II
1. To find the area of a triangle when the sides of a triangle are known .
*2. To pick the largest of three given numbers.
*3 . To solve a quadratic equation.
*4. To do income tax calculation.
UNIT III
*5. To find the average height of boys and girls in a class.
6. To add the digits of a given integer and to reverse it.
*7. To print the result of students in an examination.
8. To compute discount.
9. To find the number of days in the months of a year.
UNIT IV
10.To find the average of n given numbers.
*11.To find the biggest of n given numbers.
*12.To arrange the n given numbers in ascending / descending order.
UNIT V
13.To determine the value of a given function.
14.To calculate the interest for various amounts.
*15.To determine n! and use it to find ncr and npr.
16.To evaluate a second order determinant and use it to determine the value of a third order
determinant.
*17.To add or subtract two given matrices.
*18.To multiply two given matrices.
*PROGRAMS FOR PRACTICALS.
************
39

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPALLI-2.
DEPARMTENT OF MATHEMATICS
SEMESTER - IV
ALLIED ( OPTIONAL ) CALCULUS AND TRIGONOMETRY
No.of.Hours: 5 Max.Marks: 100
No.of.Credits: 5 Code:CU5MA:EA4B/CU5MA:EA6C
UNIT I:
TRIGONOMETRY:
Expansions of Cosnθ, Sinnθ and Tannθ (n being a positive integer) – Expansions of Sinnθ
and Cosnθ in a series of sines and cosines of multiples of θ (n being a positive integer and θ in
radians) – Expansions of Sinθ, Cosθ and Tanθ in a series of powers of θ – approximations
(Formation of equations excluded)
UNIT II:
Hyperbolic functions, inverse hyperbolic functions, separation into real and imaginary parts,
Logarithms of complex numbers of the form x+iy and general value of logarithms.
UNIT III :
DIFFERENTIAL CALCULUS:
Successive differentiation – nth derivative of standard functions – Leibnitz theorem (without
proof) Application to simple problems – Jacobians of two and three variables.
UNIT IV :
PARTIAL DIFFERENTIAL EQUATIONS:
Solutions of first order equations in their standard forms – F(p,q) = 0, F(x,p,q) = 0, F(y,p,q)
= 0, F(z,p,q) = 0,F(x,p) = F (y,q), Z = px+qy+f(p,q), Lagrange’s equations Pp+Qq = R
UNIT V:
FOURIER SERIES:
Fourier series-full range and half range series.
BOOKS FOR STUDY:
UNIT I,II,III,IV : ANCILIARY MATHEMATICS BY S.NARAYANAN AND
T.K.MANICAVACHAGOM PILLAY.
UNIT V: ENGINEERING MATHEMATICS(THIRD YEAR-PART- B) BY
Dr.M.K.VENKATRAMAN
40

SEMESTER - V
ALLIED( OPTIONAL) ANALYTICAL GEOMETRY OF 3D, VECTOR CALCULUS &
LAPLACE TRANSFORMS
No. of Credits: 5 Code:CU5MA:OA5B
UNIT I:
Analytical Geometry of Three Dimensions:
Cartesian co-ordinates – distance between points – Direction Cosines – Direction ratios –
angle between two lines - The Plane – the general equation of the plane – Standard forms of
equations of planes.
UNIT II:
Skewlines – Shortest distance between two skewlines – equation of the line of shortest
distance (Cartesian only) – coplanarity of Straight lines Sphere. General equation – tangent planes
– section of a sphere by a plane - sphere through a given circle.
Vector Calculus:
UNIT III:
Vector differentiation: Velocity – acceleration – scalar and vector fields – Gradient, Divergence
and curl – applications - Laplacian operator.
UNIT IV:
Laplace Transform:
Laplace transforms of the functions eat
, e-at
, cosat, sinat, tn
, e-at
cosbt, e-at
sinbt, e-at
tn
,
f’(t), f”(t), fn
(t) (where n is a positive integer)
UNIT V:
Inverse Transforms:
Inverse transforms relating to the above standard functions – application to solution of ordinary
TREATMENT as in
UNIT I & II : Ancillary Mathematics by S. Narayanan
UNIT III : Vector analysis by K. Viswanathan and S. Selvaraj.
UNITS IV & V: Ancillary Mathematics (Volume I – Part II Section B) by Narayanan and T.K.
Manicavachagom Pillay.
41

SEMESTER - VI
ALLIED (OPTIONAL) NUMERICAL AND STATISTICAL METHODS
No. of Credits: 5 Code:CU5MA:EA6B
UNIT I:
Solving algebraic and transcendental equations – Bisection, False position and Newton
-Raphson methods.
UNIT II:
Interpolation:
Newton’s Forward and backward interpolation formulae-Lagrange’s Interpolation formula.
UNIT : III
Numerical differentiation and integration:
Introduction - Numerical differentiation - Maximum and minimum values of a tabulated function -
Numerical integration – Trapezoidal rule - Simpson's 1/3-rule.
Unit IV: Statistics
Measures of dispersion – Range – Quartile deviation – Mean deviation – Standard deviation
and their coefficients.skewness-measures of skewness-Karl pearson’s coefficient of skewness-
Bowley’s coefficient of skewness
Unit V:
Moments-kurtosis-Association of attributes-Yule’s coefficient of association
Note : Derivations not included Numerical problems only.
BOOK FOR STUDY:
Treatment as in "Introductory methods of Numerical Analysis" ( Third Edition, Twenty third
printing, June, 1998) By S.S.Sastry
UNIT - I: Chapter 2. Sections 2.1, 2.2, 2.4 & 2.5(2.5.1 omitted)
UNIT - II: Chapter 3. Sections 3.6 ,3.9 & 3.9.1
UNIT - III:Chapter 5. Sections 5.1, 5.2(5.2.1 omitted) 5.3, 5.4.1,5.4.2
BOOK FOR STUDY:
42

UNIT IV,V: - Statistics by R.S.N. Pillai and Bagavathy
***********
HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI -2
SEMESTER – III/V
I.D.COURSE : MATHEMATICS FOR COMPETITIVE EXAMINATIONS
No. of Hours : 4 Max.Marks:100
No. of Credits: 4 Code:CU5MA:OI1
UNIT: I
Number system - Sum and difference, Multiplication and division, squares and square roots,
L.C.M. & H.C.F. of 2 or more numbers, Fractions and Decimal fractions - A.P. & G.P.
UNIT: II
Problems involving ratio and proportion - Profit and Loss -Percentage – Averages.
UNIT: III
Time and work - Time and Distance - Problems involving boats and streams - trains- cisterns and
pipes.
UNIT: IV
Simple interest, compound interest and partnership.
UNIT: V
Formulae - results relating to perimeters and areas of square, rectangle, Circle, Triangle, Cube,
Sphere, Cone & Cylinder – Data Interpretation -Bar chart - Pie Diagram.
REFERENCES :
Text books of Matriculation School.
Arithmetic for Competitive Examinations by R.S.Aggarwal.
Arithmetic for Competitive Examinations by V.K. Subburaj.
Competition Success Review for Bank Probationary Officer's Exam.
Competition Success Review for MBA entrance Examinations.
43

HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPALLI-2.
DEPARMTENT OF MATHEMATICS
SEMESTER – IV
I.D. COURSE - ELEMENTARY NUMERICAL METHODS
No.of Hours : 4 Max.Marks: 100
No. of Credits : 2 Code: CU5MA:EI2
UNIT - I:
Solution of Algebraic and Transcendental Equations:
Introduction - The Bisection method - The method of false position - Newton _ Rapshon method.
UNIT - II:
Interpolation:
Introduction - Finite differences - Forward differences – Backward differences - Newton's formulae
for interpolation - shift operator - Lagranges interpolation formula ( with out proof)
UNIT - III:
Numerical Differentiation:
Numerical differentiation of first order only.
UNIT - IV:
Solution of Linear System of Equations:
Matrix inversion method - Gaussian elimination method - Gauss - Jordan method.
UNIT - V:
Numerical solution of ordinary differential equations:
Solution by Taylor's series method - Euler's method - R.K. method of second order and fourth order
( Problems only).
Treatment as in "Introductory methods of Numerical Analysis" ( Third Edition, Twenty third
printing, June, 1998) By S.S.Sastry
UNIT - I: Chapter 2. Sections 2.1, 2.2, 2.4 & 2.5
UNIT - II: Chapter 3. Sections 3.1, 3.3.1, 3.3.2, 3.6 & 3.9.1
UNIT - III:Chapter 5. Sections 5.2
UNIT - IV: Chapter 6. Sections 6.3.1, 6.3.2
UNIT - V: Chapter 7. Sections 7.2, 7.4, 7.5
44

SEMESTER – IV/VI
I.D. COURSE:DECISION MAKING TECHNIQUES.
No. of Hours:4 Max.Marks:100
No.of.credits:4 Code: CU5MA:EI3
Unit I :(Chapter 2: 2.1 – 2.5)
Introduction to Linear Programming Problem – Mathematical formulation – Graphical Solution
Method.Definitions of objective functions,constraints,non negative restrictions,solution,feasible
solution and optimal solution
Unit II : ( Chapter 9: 9.1 to 9.6)
Introduction to Game Theory – Two person zero sum game – The maximin– minimax principle –
Games without saddle – Solution of 2 x 2 rectangular games – Graphical method.
Unit III: (Chapter 6: 6.5,6.9)
Transportation Problem –Definition – Mathematical formulation-Initial basic feasible solution –
North –West Corner rule-Row Minima Method-Column Minima Method-Matrix Minima Method-
Vogel’s Approximation Method – Unbalanced Transportation Problem-Maximization type.
Unit IV: (Chapter 18: 18.1, 18.2, 18.4 – 18.6,18.7(Cases(1and 2)0nly)
Inventory Control – Types of inventory – Economic order quantity – Deterministic inventory
problem (with and without shortages(instantaneous replenishment only))– EOQ problem with price
breaks.
Unit V: (Chapter 21: 21.1 – 21.7)
Network scheduling PERT – CPM – time calculation in Networks – Critical Path Method (CPM) –
PERT calculation. (Expected value and variance of μi only)
Treatment as in Operations Research by KantiSwarup, Gupta and ManMohan.
45

REFERENCE BOOKS:
1. Problems in Operations Research by P.K.Gupta and D.S.Hira
2.Operations Research by Hamdy, Taha ,Prema Publishers,1995,Bangalore
HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI -2
CERTIFICATE COURSE
APTITUDE MATHEMATICS
No. of Hours :30/Semester Max.Marks:100
UNIT: I
Number system – Simplification using formulae and rules.- L.C.M. & H.C.F. of 2 or
more numbers – Odd man out and Series (A.P. and G.P. –nth term and sum only )
UNIT: II
Problems involving Ratio and Proportion - Profit and Loss .
UNIT: III
Percentage - Average - Mixture or allegation.
UNIT: IV
Time and work - Cisterns and Pipes –Data Analysis.
UNIT: V
Time and Distance - Problems involving Boats and Streams – Trains.
TREATMENT as in Arithmetic (Subjective and Objective ) for Competitive
Examinations by R. S.Agarwal, S. Chand and Company Ltd., Ram Nagar, New
Delhi.
UNIT I : CHAPTERS 1,2,4 AND 30
UNIT II : CHAPTERS 8,9 AND 16
UNIT III: CHAPTERS 6,7 AND 17
UNIT IV : CHAPTERS 11, 12, AND 29
UNIT VI : CHAPTERS 13,14 AND 15.
REFERENCES :
Text books of Matriculation School.
Arithmetic for Competitive Examinations by V.K. Subburaj.
Competition Success Review for Bank Probationary Officer's Exam.
Competition Success Review for MBA entrance Examinations.
46

(SHIFT II)
HOLY CROSS COLLEGE (AUTONOMOUS) TIRUCHY – 620 002.
CURRICULUM STRUCTURE (CAFETERIA)
B.SC. MATHEMATICS WITH SPECILIZATION IN
COMPUTER APPLICATIONS
( 2005 – 2008) (2006-2009)
1. Foundation Courses F
2. Major Compulsory and Optional courses M
3. Allied Compulsory and Optional courses A
4. Interdisciplinary Courses ID
5. Extra Projects and Placements.
Sem Com
Ponent
Code No Course Subject Title Hrs/
Week
Credits
1 F1 CU5T:01 Language 1 –
Paper 1
5 5
F2 CU5E:01 Language II –
Paper 1
6 6
F3 RESCAPES Capacity Building 1 1
F4 Life Oriented
Education
1
M1 CU5MA:OM1 Major Core Calculus and Fourier
Series
7 7
M2 CU5MA:OM2 Major Core Classical Algebra
&Trigonometry
6 6
A1 CU5MA:OA1A Allied Compulsory-
Paper 1
Mathematical Statistics-I 5 5
TOTAL 30 31
II F1 CU5T:E2 Language 1 –
Paper II
5 5
Paper II
6 6
F3 RESCAPES Environmental Studies 4
F4 Life Oriented
Education
1 1
M3 CU5MA:EM3 Major Core Analytical Geometry of
Three Dimensions and
7 7
47

Vector Calculus
M4 CU5MA:EM4 Major Core Sequences and Series 6 6
A2 CU5MA:EA2A Allied Compulsory
Paper II
Mathematical Statistics
-II
5 5
TOTAL 30 34
III F1 CU5T:O3 Language I -
Paper III
5 5
F2 CU5E:O3 Language II –
Paper III
6 6
F3 RESCAPES Environmental
Sustenance Project
-- 1
F4 Life Oriented
Education
1 1
M5 CU5MA:OM5 Major Core Statics 4 4
M6 CU5MA:OM6B Major Core Programming in
Fortran 90
5 5
A3 CU5MA:OA3A Allied Compulsory
Paper III
Mathematical
Statistics -III
5 5
Course
4 4
TOTAL 30 31
IV F1 CU5T:E4 Language I –
Paper IV
5 5
Paper IV
6 6
F3 RESCAPES Environmental
Sustenance Project
1
F4 Life Oriented
Education
1 1
M7 CU5MA:EM7 Major Core Dynamics 4 4
M8 CU5MA:EM8B Major Core Programming in C for
Numeric Methods
5 5
A4 Allied Optional
Paper I
5 5
Course
4 4
TOTAL 30 31
V F3 RESCAPES Impact Study 1
F4 Life Oriented
Education
1 1
M9 CU5MA:OM9 Major Core Real Analysis 5 5
M10 CU5MA:OM10B Major Optional Programming in C++ 5 5
M11 CU5MA:OM11B Major Optional Differential Equations &
Laplace Transforms
5 5
M12 CU5MA:OM12B Major Optional Visual Programming 5 5
A5 Allied Optional
Paper II
5 5
48

Course
4 4
Sem
Com
Ponent
Code
TOTAL
Course Subject Title
30
Hrs/
Week
31
Credits
VI F3 RESCAPES Project
(optional)
F4 Life Oriented
Education
1 1
M13 CU5MA:EM13 Major Core Theory of Functions of a
Complex Variable
5 5
M14 CU5MA:EM14B Major Optional Statistical Packages 5 5
M15 CU5MA:EM15B Major Optional Algebra 5 5
M16 CU5MA:EM16B Major Optional Discrete Mathematics 5 5
A6 Allied Optional
Paper III
5 5
Course
4 4
TOTAL 30 30
SEMESTER – WISE CREDIT DISTRIBUTION
I SEMESTER 31
II SEMESTER 34
III SEMESTER 31
IV SEMESTER 31
V SEMESTER 31
VI SEMESTER 30
--------
Total 188
--------
49

B.Sc., MATHEMATICS
SEMESTER – I
MAJOR (CORE) CALCULUS AND FOURIER SERIES
UNIT I:
Successive differentiation – Leibnitz theorem (with proof) – Curvature – radius of curvature
– centre of curvature – circle of curvature (both in Cartesian and polar coordinates) and evolute.
UNIT II:
Partial differentiation – Total differential coefficient – Homogeneous functions-Partial
derivatives of a function of two functions – Jacobian of two and three variables-Maxima and
minima of functions of two variables.
UNIT III:
sinn
x dx, 0 ∫π/2
cosn
x dx, 0 ∫π/2
sinn
x cosn
x dx
Multiple integrals – Evaluation of double integrals in cartesian and polar co-ordinates. Triple
integrals (evaluation in Cartesian Co-ordinates only) - Change of order of Integration.
UNIT IV:
Beta and gamma functions – Definition, recurrence formula of gamma functions – Properties
of Beta functions-Relations between Beta and Gamma functions – Evaluation of simple integrals.
UNIT V:
Fourier cosine and sine series – Half range Cosine and Sine series.
TREATMENT as in
CALCULUS (Vol I) by S. Narayanan and T.K. Manicavachagom Pillay for units
I and II.
50

Unit I – Chapter III, Chapter X Sec2 (from 2.1 to 2.6)
Unit II- Chapter VIII (Sec 1 and Sec.4)
CALCULUS (Vol II) by S. Narayanan and T.K. Manicavachagom Pillay for units III and IV
Unit III- Chapter V Sections 1 to 4
Unit IV – Chapter VII Sections 2,3,4,5
Engineering Mathematics – Third year (Part B), 11th
Edition by Dr. M.K. Venkatraman for
unit V.
Unit V – Chapter I (Section 1 to 6, Section 8, Section 10)
REFERENCES:
Schaums Outline series – Theory and problems of Advanced Calculus.
Differential and Integral Calculus by N. PISKUNOV Mir Publishers.
Advanced Calculus – David V. Widder – Prentice Hall of India
(II Edition)
Calculus and Analytic Geometry – Thomas/Finney Narosa Publishing House.
Calculus with Computer Applications:- Ransom V. Lynch,
Donald R. Ostberg & Robert G. Kuller.
Xerox College Publishing.
Schaums’ Outline series – Theory and Problems of Laplace Transforms.
********************************
51

B.Sc., MATHEMATICS
SEMESTER – I
MAJOR ( CORE ) CLASSICAL ALGEBRA AND TRIGONOMETRY
CLASSICAL ALGEBRA
UNIT I:
Theory of Equations:
Relation between roots and coefficients – symmetric functions of roots in terms of the
coefficients –Sum of the powers of the roots of an equation-Newton’s Theorem on the sum of the
powers of the roots - Transformation of equations – Reciprocal equations – To increase or Decrease
the roots by a given quantity – Removal of terms – To form an equation whose roots are any power
of the roots of a given equation - Descarte’s rule of signs.
UNIT II:
Theory of Numbers:
Introduction – Divisors of a given number N – Euler’s function Ø (N) – highest power of a
prime p contained in n! – congruences – numbers in arithmetical progression – Fermats’ theorem-
Wilson’s theorem – Lagranges’ theorem.
TRIGONOMETRY
UNIT III:
Expansions of Cosnθ, Sinnθ, tannθ where n is a positive integer (excluding formation of
equations); Expansions of Cosn
θ, Sinn
θ in a series of sines and cosines of multiples of θ, (θ in
radians) and expansion of Cosθ, Sinθ, tanθ in a series of powers of θ – approximations.
52

UNIT IV:
Hyperbolic functions – in verse hyperbolic functions, separation into real and imaginary
parts. Logarithm of complex numbers x+iy – general value of logarithm.
UNIT V:
Summation of trigonometric series-method of differences – sum of sines of n angles in A.P.
– sum of cosines of n angles in A.P. – summation of series using complex quantities.
TREATMENT as in:
UNIT I: Algebra Vol I by T.K. Manicavachagom Pillay, T. Natarajan and K.S. Ganapathy
Chapter 6 Sec: 11 to 21,24.
UNIT II: Algebra Vol II by T.K. Manicavachagom Pillay, T. Natarajan and K.S. Ganapathy
Chapter 5 fully.
TREATMENT as in Trigonometry by Narayanan and Manicavachagom Pillay for UNIT III,
IV & V.
UNIT III: Chapter III (Formation of Equations Excluded)
UNIT IV: Chaper IV and in Chapter V (Sec 5 only)
UNIT V: Chapter VI (Sec. 1 to Sec.3)
REFERENCES:
3. Set Theory, Number System and Theory of Equations by Arumugam and
Thangapandi Issac, New Gamma Publishing House.
4. Trigonometry by P.R. Vittal, Margham Publisher.
3. Trigonometry by P.P. Gupta, Oxford University Press.
4. Trigonometry by P. Duraipandian, Emerald Publications.
****************************
53

B.Sc., MATHEMATICS
SEMESTER –II
MAJOR( CORE) ANALYTICAL GEOMETRY OF THREE DIMENSIONS AND VECTOR
CALCULUS
No. of Credits: 6 CODE:CU5MA:EM3
UNIT I:
Cartesian coordinates- Distance between points – Direction Cosines – Direction ratios –
angle between two lines. The plane – the general equation of the plane – standard forms of
equations of planes – Equation of the plane in the form P+ λ P’ = Ø Bisector planes.
UNIT II:
Different forms of equations of a straight line – the plane and the straight line – coplanar
lines – the shortest distance between two skew lines – equations of two skew lines.
UNIT III:
Equation of a sphere – Length of the tangent from a point – Tangent planes. The plane
section of a sphere - Intersection of two spheres.
VECTOR CALCULUS
UNIT IV:
Differentiation:
Derivatives of vector functions – velocity and acceleration – differential operators –
directional derivatives, gradient, divergence and curl – solenoidal and irrotational vectors – vector
identities.
54

UNIT V:
Integration:
Integration of vector functions – velocity and acceleration – Line integrals – work done by a
force – conservative field – surface integral and its applications – volume integral and its
applications – Integral theorems (without proof ) - Gauss divergence theorem, Green’s theorem,
Stoke’s theorem and their applications.
Treatment as in “A Text Book of Analytical Geometry (Part II – Three Dimensions) By
T.K. Manicavachagom Pillay and T. Natarajan. Revised Edition 1996, Reprint July – 2000.
UNIT I: Chapters I and II
UNIT II: Chapter III (excluding sections 9,10 & 11)
UNIT III: Chapter IV for the Sphere
Reference:
Analytical Geometry (3 –Dimensional) by P.Duraipandian,Laxmi Duraipandian & D.Mahilan –
Emerald Publishers(1990)
For Vector calculus, Treatment as in “Vector Calculus” By K. Viswanathan and S. Selvaraj –
Emerald Publishers)
UNIT IV: Chapters 1 and 2
UNIT V: Chapters 3 and 4.
Reference:
Vector Analysis by P.Duraipandian ,Laxmi Duraipandian –Emerald
Publishers (1998)
************************************
55

B.Sc., MATHEMATICS
SEMESTER –II
MAJOR (CORE) SEQUENCES AND SERIES
No. of Credits: 6 Code: CU5MA:EM4
UNIT I:
Sequences – sets – Sequences – Limit of a sequence – bounded sequences – Cauchy’s
general principle of convergence – monotonic sequence.
UNIT II:
Infinite Series- definition of convergence, divergence and oscillation – some general
theorems – convergence of 1/ n p
and Geometric Series.
Tests of convergence.
5. Comparison tests
6. Cauchy’s condensation test
7. D’Alembert’s Ratio Test
8. Cauchy’s Root test
9. Raabe’s test (simple problems only)
UNIT III:
Alternating Series : Absolute convergence – conditional convergence – Leibnitz’s test and
simple problems.
Binomial theorem for rational index – summation of series and approximations:
UNIT IV:
Exponential and Logarithmic Series – summation and approximations.
UNIT V:
56

General summation of series – Application of partial fractions –summation by difference
series – recurring series.
TREATMENT as in Algebra –volume I by Manicavachagom Pillay, Natrarajan & Ganapathy.
UNIT I: Chapter 2 – Section 4, Section 6, Section 7.
UNIT II: Chapter 2 – Section 8 to Section 20.
UNIT III: Chapter 2 – Section 21 to Section 24.
Chapter 3 – Section 5,10 & 14.
UNIT IV: Chapter 4
UNIT V: Chapter 5
REFERENCES:
4. A first course in Real Analysis by M.K. Singal and Asha Rani Singal,
R. Chand & Co, New Delhi.
5. Sequences and Series by Dr. Arumugam.
******************************
57

HOLY CROSS COLLEGE ( AUTONOMOUS) TIRUCHIRAPPALLI – 620 002.
B.SC., MATHEMATICS
SEMESTER III.
MAJOR (CORE) STATICS
No. of Hours: 4 Max.Marks:100
No. of Credits:4 Code:CU5MA: OM5
Unit : I
Force – Types of Forces – Equilibrium – Forces acting at a point Parallelogram of forces – Triangle
of forces Ploygon of forces - Lami’s theorem – Resolution of a force – Composition of forces –
Resultant – Conditions of equilibrium.
Unit: II
Parallel Forces – Like and Unlike parallel forces – Resultants – Moment of a force about a point -
Varignon’s Theorem on Moments – Principle of Moments – Moment of a force about an axis –
Couples – Equilibrium of two couples – Equivalence of two couples – Couples in Parallel Planes –
Resultant of Coplanar Couples – Resultant of a couple and a force.
Unit : III
Equilibrium of Three Forces acting on a rigid body – Three coplanar forces – conditions of
Equilibrium – Two trigonometrical theorems useful in the solution of statical problems – Problem
solving.
Unit : IV
Friction – Laws of friction – angle of friction – cone of friction – equilibrium of a body on a rough
inclined plane – Problems involving the force of friction.
Unit : V
Equilibrium of strings – Common catenary – equations – tension at any point – geometrical
properties – Parabolic catenary – Suspension Bridge.
Treatment as in Statics by Dr. M.K. Venkataraman, Agasthiar Publications, Trichy (1996).
Unit: I - Chapters 1 & 2
Unit: II – Chapters 3 & 4
Unit: III – Chapter 5
Unit: IV – Chapter 7
Unit: V – Chapter 11
BOOKS FOR REFERENCE
1. Statics by A.V. Dharmapadam
2. Mechanics by P. Durai Pandian & Others.
58

B.SC. MATHEMATICS
SEMESTER : III
MAJOR (CORE) PROGRAMMING IN FORTRAN 90
No. Of. Hrs:5 Code:CU5MA:OM6B
No. of Credits:5 Max. Marks:100
UNIT I
FORTRAN constants and variables - Arithmetic operators - Integer expressions - Real expressions -
precedence of operators in expressions - Assignment statements - Intrinsic functions .
UNIT II
List directed input and output statements-Relational operators - Block IF construct - Implementing
Loops In Program .
UNIT III
The Block Do loop count controlled Do loop - Rules regarding Do loops.
Logical constants, variables and expressions. Precedence rules for logical operators - The case
statement.
UNIT IV
Format description for numerical DATA-Format description for PRINT Statement - Multi record
formats Reading and Writing logical quantities - Generalised Input/Output statements - Processing
of string characters. The character Data Type - manipulating strings - Comparing character strings.
UNIT : V :
Introduction - Function subprograms. Syntax rules for Function subprograms - Generic Functions.
Subroutines - Internal Procedures - Arrays variable - Use of multiple subscripts - Do type notation
for Input/Output statements - Initializing arrays - use of Arrays in Do loops.
TREATMENT AS IN COMPUTER PROGRAMMING IN FORTRAN
90 AND 95 BY V. RAJARAMAN
UNIT I : CHAPTERS 3 & 4 (OMIT 4.8)
UNIT II :CHAPTERS 5AND 6
UNIT III : CHAPTERS 7 AND 8
59

UNIT IV : CHAPTERS 11 AND 12
UNIT V : CHAPTERS 9 AND 10 (OMIT 10.7 AND 10.8)
PRACTICALS:
I DAY:
Simple programs using READ and PRINT statements.
1. WRITE A PROGRAM TO CALCULATE SIMPLE INTEREST AND COMPOUND
INTEREST.
2. WRITE A PROGRAM TO FIND AREA OF TRIANGLE, SQUARE, RECTANGLE, CIRCLE,
SURFACE AREA OF SPHERE, CONE AND CYLINDER.
3. PROGRAM TO CONVERT CENTEGRADE TO FAHRENHET.
II DAY:
Programs using IF statement
1. PROGRAM TO FIND THE BIGGEST / SMALLEST OF THE GIVEN
3 NUMBERS.
2. PROGRAM TO CALCULATE THE AVERAGE MARK OF EACH STUDENT IN THE
GIVEN THREE TESTS.
3. PROGRAM TO SOLVE A GIVEN QUADRATIC EQUATION.(using arithmetic IF)
IIIDAY:
Programs using DO..CONTINUE statements
1. PROGRAM TO FIND THE SUM OF, SUM OF SQUARES OF SUM OF
CUBES OF FIRST "N" NATURAL NUMBERS.
2. PROGRAM TO FIND THE SUM OF ANY GIVEN "N" NUMBERS.
3. PROGRAM TO FIND THE SUM OF EVEN / ODD NUMBERS
FROM 1 TO N
IV DAY:
Programs using array - DIMENSION statement
1. PROGRAM TO ARRANGE THE GIVEN SET OF "N" NUMBERS IN ASCENDING /
DESCENDING ORDER.
2. PROGRAM TO FIND THE BIGGEST / SMALLEST OF THE GIVEN N ELEMENTS IN
AN ARRAY.
3. PROGRAM TO FIND THE NUMBER OF POSTIVE, NEGATIVE AND ZERO ELEMENTS
IN AN ARRAY OF N ELEMENTS.
V DAY:
Programs using SUBPROGRAM
1. PROGRAM TO FIND ncr and nPr
2. PROGRAM TO FIND SINX=X-X /5!..... AND COSX=1-X /4! - .... AND COMPARE
WITH BUILT-IN-FUNCTIONS.
3. PROGRAM TO ADD, SUBTRACT AND MULTIPLY TWO GIVEN MATRICES ,
TRACE OF A MATRIX.
60

B.SC. MATHEMATICS
SEMESTER : IV
MAJOR (CORE) DYNAMICS
No. Of. Hrs: 4 Max. Marks:100
No. of Credits:4 CODE: CU5MA:EM7
Objective:
UNIT: I
Momentum – Newton’s Laws of Motion – Absolute units of forces – Conservation of linear
momentum – Motion of a particle on planes – Motion of connected particles.
UNIT : II
Projectiles – Path of a projectile – Characteristics of the motion of a projectile – Greatest height -
Time of flight - Horizontal range – Maximum horizontal range – Directions of projection – Velocity
of the projectile – Simple problems.
UNIT : III
Motion of a projectile on an inclined plane – Range on an inclined plane – Time of flight – Greatest
distance from the inclined plane – Maximum range on an inclined plane – Directions of projection
on an inclined plane – Enveloping parabola – Simple problems.
UNIT : IV
Impulsive forces – Impact of two bodies – Motion of a shot and gun – Collision of elastic bodies –
Fundamental laws of inpact – Impact of a smooth sphere on a fixed plane – Direct impact – Oblique
impact – Simple problems.
UNIT : V
Simple harmonic motion in a straight line – Definitions – General solution of a simple harmonic
motion equation – Composition of two simple harmonic motions – Simple problems.
Treatment as in “A Text Book of Dynamics” by Dr. M.K. Venkatraman – Agasthiar Publications,
Tiruchy-2.
Eleventh Edition – February 2004.
Unit: I – Chapter IV – 4.1 to 4.18, 4.2 to 4.23
Unit:II- Chapter VI – 6.1 to 6.11
Unit:III – Chapter VI – 6.12 to 6.17
Unit:IV – Chapter VII – 7.1 to 7.5, Chapter VIII - 8.1 to 8.8
Unit:V – Chapter X – 10.1 to 10.3, 10.6, 10.7
1. Dynamics by Prof. M.L. Khanna - Jai Prakash Nathan & Company, Meerut – 10th
Edition –
1975.
2. Principles of Dynamics by Greenwood, Donald T-Prentice Hall of India-New Delhi – 1988.
3. Dynamics – K.Viswanatha Naik & M.S. Kasi – Emerald Publishers, Egmore, Chennai-2001.
61

4. Golden Dynamics by N.P. Bali – Laxmi Publishers, New Delhi – 1986.
B.SC. MATHEMATICS
SEMESTER IV
MAJOR (CORE) PROGRAMMING IN C FOR NUMERICAL METHODS
No. of Credits:5 Code:CU5MA:EM8B
UNIT - I:
Constants, variables, data types, symbolic constants - operators and expressions - evaluation of
expressions - reading and writing a character - formatted input and output - handling of character
strings - operations on strings - string handling functions.
UNIT - II:
Decision making and branching - Using IF, IF-ELSE, Nesting of IF-ELSE statements - ELSE-IF
ladder - Switch statement - the conditional operator - GOTO statement - Decision making and
looping - the WHILE, DO, FOR statements.
UNIT - III:
Arrays - one dimensional, two dimensional, multi dimensional groups - structure - definition giving
values to members - Initialization - Comparison - arrays of structures - Arrays within structures -
structures within structures and functions - Unions - Size of structures.
UNIT - IV:
User defined functions - the form of C functions - Return values and their types - calling a function -
category of functions - no arguments and no return values - Arguments but no return values -
Arguments with return values - Nesting of functions - Recursion -
Function and arrays - the scope and life time of variables in functions.
UNIT - V:
File management - Defining and opening a file - Closing a file - I/O operations on files.
Scope and Treatment as in "Programming in ANSI C " Second Edition By
E. Balagurusamy.
UNIT - I: Chapters 2,3,4 and 8
UNIT - II: Chapters 5 and 6
UNIT - III: Chapters 7 and 10
UNIT - IV: Chapter 9
UNIT - V: Chapter 12
62

REFERENCE BOOKS:
Programming in C - V.Rajaraman Programming with C - Schaum's Series
ANNEXURE
C Programming for Theory and Practicals:
I DAY:
Roots of equations : Iterative Methods
1. Bisection Method
2. False Position Mehod
3. Newton - Raphson Method
II DAY:
Solution of simultaneous equations.
1. Gauss - Elimination method
2. Gauss - Seidal Method
3. Gauss - Jordan Method
III DAY:
INTERPOLATION:
1. Lagrange's Method
2. Newton - Forward Method
3. Newton - Backward Method
IV DAY:
NUMERICAL DIFFERENTIATION:
1. Euler Method
2. Predictor - Corrector Method
3. Runge-kutta IV order method
V DAY:
1. Simpson's 1/3 rule
2. Trapezoidal rule
63

B.SC. MATHEMATICS
SEMESTER V
MAJOR (CORE) REAL ANALYSIS
No.of.Hours : 5 Max.Marks:100
No.ofCredits:5 Code:CU5MA:OM9
UNIT I : REAL NUMBERS
Introduction to Real Number system - the field axioms and theorems - Order in R - Absolute value
- Completeness - Some important subsets of R - Representation of real numbers as points on a
straight line - Intervals - Countable and uncountable sets.
UNIT II : NEIGHBOURHOOD AND LIMIT POINTS
Neighbourhoods - Open sets - Closed sets - Limit points of a set - Closure of a set - Interior of a set
- Compactness and connectedness.
UNIT III : LIMITS AND CONTINUITY
Limits - Continuous functions - Types of discontinuities - Algebra and boundedness of continuous
functions - Intermediate value theorem - Inverse function theorem - Uniform continuity.
UNIT IV : DERIVATIVES
Introduction - Derivability and continuity - Algebra of derivatives - Inverse function theorem for
derivatives - Darboux's theorem.
MEAN VALUE THEOREMS
Rolle's theorem - Mean value theorems on derivatives (Lagrange's and Cauchy's) - Taylor's
theorem with remainder - Taylor's series - power series expansions of some standard functions: e ,
Sin x, Cos x, (1+x) and log(1+x)
UNIT V : RIEMANN INTEGRATION
Introduction - Riemann integrability and integral of bounded functions over bounded intervals -
Properties of Darboux sums - Darboux's theorems I and II - Equivalent definition of integrability
and integral - Conditions for integrability - Particular classes of bounded integrable functions -
Properties of integrable functions - Integrability of sum, difference, product, quotient and
modulus of integrable functions - Continuity and derivability of the integral function -
fundamental theorem of integral calculus.
64

Treatment as in 'A First Course in Real Analysis' by M.K.Singal and Asha Rani Singal - R.Chand &
Co. New Delhi. 20TH Edition,1998
UNIT I : CHAPTER 1
UNIT II : CHAPTER 2
UNIT IV : CHAPTER 6 (Omit from section 6) and Chapter 8
( Omit sections 7 and 8)
UNIT V : Treatement as in "Elements of Real Analysis" by Shanti Narayan.
Chapter 9 (Omit Sec 9.12, 9.13, 9.16 and 9.17)
1. 'A Course of Mathematical Analysis' by Shanthi Narayan.
2. "Real Analysis" by Arumugam and others.
65

B.Sc. MATHEMATICS
SEMESTER V
MAJOR (OPTIONAL) PROGRAMMING IN C++
No.of Hours:5 MAX.MARKS:100
No.of Credits:5 Code:CU5MA:OM10B
UNIT I :
BEGINNING WITH C++: Introduction to C++-Applications of C++ statements-structure of
C++ programs.
TOKENS,EXPRESSIONS AND CONTROL STRUCTURES: Tokens, keywords,
identifiers, data types - symbolic constants - defining variables - operators in C++ - Type cast
operator-control structures-Programming examples.
UNIT II :
FUNCTIONS IN C++ : Main function-Function prototyping-call by reference-return by
reference-inline functions-default arguments-constant arguments-Function overloading, friend and
virtual functions.
CLASSES AND OBJECTS : Specifying a class – Defining member functions –Making
outside function inline – Nesting of member functions – Array within a class – Memory allocation
for objects – Static members and functions.
UNIT III :
CONSTRUCTORS AND DESTRUCTORS : Constructors – Parametrized constructors –
Multiple constructors in a class – Constructors with default arguments – Dynamic initialization of
objects – Copy constructors – Destructors.
OPERATOR OVERLOADING AND TYPE CONVERSIONS : Defining operator
overloading – Overloading unary , binary operators – binary operators overloading using friends –
rules for overloading operators – Type conversions.
UNIT IV :
INHERITANCE,EXTENDING CLASSES : Introduction – Defining derived classes –
Single Inheritance – Making a private member inheritable – Multilevel,Multiple Hierarchial
classes : Nesting of classes.
66

UNIT V :
MANAGING CONSOLE I/O OPERATIONS : Introduction – C++ streams – C++ stream
classes –Unformatted I/O Operations –Formatted console I/O operations – Managing output with
manipulators.
WORKING WITH FILES : Introduction – Classes for File stream operations – Opening and
closing of File – File modes – file pointers and their manipulators – sequential I/O operators.
PRACTICAL WORK :
1. Sorting numbers in ascending and descending order
2. Implementation of Default arguments
3. Implementation of Reference variables
4. Friend Function
5. Inline Functions
6. Virtual Functions
7. Constructor and Destructor
8. Students Marklist
9. Employee Information System
10. Operator Overloading (Comparison of two strings)
11. Single Inheritance
12. Multiple Inheritance
13. Function Overloading
TEXT BOOK :
“ OBJECT ORIENTED PROGRAMMING WITH C++”
-- E. BALAGURUSAMY ,TATA MCGRAW HILL.
BOOKS FOR REFERENCE :
1. Object oriented programming with C++ by M.A.Jayaram and D.S. Rajendra Prasad,Mumbai,
Himalaya Publishing,2002.
2. Programming with C++ by D.Ravichandran ,New York, Mc graw Hill,1999.
3. Programming in C++ by Maria Litvin and Gary Litvin ,New Delhi,Vikas Publishing House
Pvt. Ltd.,2001.
4. Programming in C++ by Nell Dale,Chip Weems and Mark Headington,New Delhi, Narosa
Publishing House,1999.
67

HOLY CROSS COLLEGE ( AUTONOMOUS) TIRUCHIRAPPALLI – 2.
B.SC. MATHEMATICS
SEMESTER V
MAJOR (OPTIONAL) DIFFERENTIAL EQUATIONS AND LAPLACE TRANSFORMS
No.of.Hours: 5 Code:CU5MA:OM11B
No.of Credits:5 Max.Marks: 100
UNIT I :
ORDINARY DIFFERENTIAL EQUATIONS
Linear homogeneous equations with variable coefficients. Equations reducible to the linear
homogeneous equation. Method of variation of parameters.
UNIT II :
PARTIAL DIFFERENTIAL EQUATIONS
Formation of partial differential equations by eliminating arbitrary constant and functions -
solutions - General, particular and complete integrals - solutions to first order equations in four
standard forms –
F(p, q) = 0, F(z,p,q) = 0, F(x,p,q) = 0,F(y,p,q) = 0, F1 (x,p) = F2 (y,q),
z = px+qy+f (p,q), Lagranges method of solving linear equation Pp + Qq = R.
UNIT III :
LAPLACE TRANSFORMS
Definition - Laplace transforms of functions eat
, Cosat, Sinat, tn
(n is a +ve integer), eat
cosbt,
eat
sinbt, f'(t), f''(t), fn
(t), tn
f(t), f(t)/ t
UNIT IV :
INVERSE TRANSFORMS
Inverse transforms relating to the above standard functions - application to solution of ordinary
UNIT V :
Second order linear partial differential equation with constant coefficients - Particular integrals for
functions of the type e ax + by
, Sin (ax + by), Cos (ax + by), xr
ys
Application of partial differential equations - Solution to heat and wave equations by method of
separation of variables (No derivation of equations)
Treatment as in Differential Equations by Narayanan & Manicavachagom Pillay for Units I, II & III
UNIT:I Chapter V - Section 5 & 6 and Chapter VII - Section 4
UNIT:II Chapter XII ( Omit from Section 5.5)
UNIT:III Chapter IX – Sections 1 to 5
UNIT:IV Chapter IX – Sections 6 to 9
Treatment as in ENGINEERING MATHEMATICS Part B by Dr.M.K.Venkatraman for Unit V.
UNIT:V Chapter 2 ( Section 13 to Section 19 ) & Chapter 3
( Omit from Section 10 )
68

B.SC., MATHEMATICS
SEMESTER - V
MAJOR (OPTIONAL) VISUAL PROGRAMMING
No. of Hours:5 Max.Marks:100
No. of Credits: 5 Code:CU5MA:OM12B
Unit I:
Introducing Visual Basic:
Starting and exiting Visual Basic – Using the Project Explorer – Working with forms – Using the
Properties Window – Using the Toolbox –Working with Projects – Printing Projects – building and
running Applications.
Adding Code and Using Events:
Using the code Window – Using naming Conventions – Using Variables – Using scope – Using
Subroutines and Functions.
Unit II:
Using Intrinsic Visual Basic Controls: Using the Label & Textbox Controls – Using the Command
Button control – Using the Frame, Check Box Option, Button controls-Using the ListBox & combo
Box Controls – using the Drive Listbox. Directory ListBox & File ListBox Controls – Using
formatting Controls – Using Control arrays- Using Tab Order.
Working with Strings: Using strings-converting Strings-concatenating strings-Manipulating strings-
comparing strings.
Working with Numbers: Using Numeric Values- Using Numeric Operators-Using Math Functions-
Using Random Numbers.
Unit III:
Using Control Statements: Using the IF & IIF Statements-using the select Case Statement –using
the DO Statement – using the FOR Statement – Using the Exit Statement.
Using Dialog Boxes: Using the Msg Box functions – Using the Input Box Functions –Using the
Common Dialog Control –Using the Common Dialog Control Open & Save as Dialog Boxes –
Using the Common Dialog Control Color Dialog Box – Using the Common Dialog Control Font
Dialog Box – Using the Common Dialog Control Print Dialog Box – Using the Common Dialog
Control Show help method.
Using Menus in Visual Basic applications: Creating Menus-Adding Code to Menus-Creating
Shortcut Menus.
Unit IV:
69

Multiple forms: The SDI and MDI styles- Image Control-Comparing the Picture box and Image
Controls-Working with Scroll Bars: Introducing scroll Bars-Building an Application –
Entering the Code-The Timer Controls-Working with arrays-Multidimentional
Arrays: Introduction to Multidimentional Arrays-Using the Grid Control-Calling general
Procedures-Internal Functions.
Unit V:
DataBase Programming with VB: Understanding DataBases and DataBase management system-
understanding relational concepts-using the Visual data Manager – validating data-Entering data-
Accessing fields in Recordset-Introduction to SQL – Advanced Data Bound Controls.
Book for Study:
UNITS I, II, III (Chapters:1-8): Scott Warner. “Teach Yourself Visual Basic 6”, Tata Mc Graw –
Hill Edition.
UNIT IV (Days 8, 14,22 & Pages (301-315 and 351-357) : Greg Perry, “SAMS Teach Yourself
Visual Basic 6 in 21 days”, Techmedia.
Unit V (Chapter:17): Evangelous Petroutstrup, “Visual Basic 6”.
Book for Reference:
Gary Cornell, “Visual Basic 6 from the Ground up”
70

B.SC. MATHEMATICS
SEMESTER VI
MAJOR (CORE) THEORY OF FUNCTIONS OF A COMPLEX VARIABLE
No.of Hours : 5 MAX.MARKS:100
No.of Credits:5 Code:CU5MA:EM13
UNIT I : Analytic functions
Introduction - Defintion - Continuous functions - Convergence of sequences and series absolute
convergence - Uniform convergence - Cauchy - Riemann equations.
UNIT II : Bilinear Transformations:
Elementary transformation - Bilinear transformation - Cross ration - Fixed points of Bilinear
transformation - some special bilinear transformation.
UNIT III : Integration in the complex plane :
Complex integration - Cauchy's integral theorem (Riemann’s proof only) and its extension
- Cauchy's integral formula - Derivative of analytic functions - Morera's theorem - Cauchy's
inequality for fn
(z0 ) Liouville's Theorem.
UNIT IV : Expansion of functions in Power Series
Taylor's theorem - Laurent's theorem - Singular points - Zeros - Pole - Essential singularity -
Meromorphic function - Principle of the argument - Rouche's theorem - Fundamental Theorem
of Algebra.
UNIT V : Residue Theorem and Contour Integration:
Residue at a pole - Residue theorem - Evaluation of Definite Integrals. between limits(-∝, ∝)
Extension of the Result- Jordan's lemma ( Statement only)- Evaluation of ∫ Sinax f(x) dx
∫ Cosax f(x)dx where a > 0 and (i) f(z) does not have a pole on the real axis
71

2006 2009 batch(cu5 ma)

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